Why is operator!= removed in C++20 for many standard library types?

In C++20 the way that the relational operators work was changed, notably with the introduction of the spaceship <=> operator. In particular, If you only provide operator==, then a != b is rewritten to !(a == b).

From [over.match.oper]/3.4:

The rewritten candidate set is determined as follows:

• For the relational ([expr.rel]) operators, the rewritten candidates include all non-rewritten candidates for the expression x <=> y.
• For the relational ([expr.rel]) and three-way comparison ([expr.spaceship]) operators, the rewritten candidates also include a synthesized candidate, with the order of the two parameters reversed, for each non-rewritten candidate for the expression y <=> x.
• For the != operator ([expr.eq]), the rewritten candidates include all non-rewritten candidates for the expression x == y.
• For the equality operators, the rewritten candidates also include a synthesized candidate, with the order of the two parameters reversed, for each non-rewritten candidate for the expression y == x.
• For all other operators, the rewritten candidate set is empty.

And [over.match.oper]/9:

If a rewritten operator== candidate is selected by overload resolution for an operator @, its return type shall be cv bool, and x @ y is interpreted as:

• if @ is != and the selected candidate is a synthesized candidate with reversed order of parameters, !(y == x),
• otherwise, if @ is !=, !(x == y),
• otherwise (when @ is ==), y == x,

in each case using the selected rewritten operator== candidate.

As such, an explicit overload for operator!= is no longer necessary. The removal of the operator has not changed comparison semantics.

All containers have had their operator!= removed, as far as I can tell (check e.g. the vector synopsis). The only exceptions are the container adaptors std::queue and std::stack: my guess is that it is to preserve backwards compatibility when used with third-party containers, in case the equality operators are not symmetric.

We don't need a library provided operator!= anymore. Providing operator== allows the compiler to do some juggling and evaluate a != b in terms of a == b, all on its own.

[over.match.oper]

3 For a unary operator @ with an operand of a type whose cv-unqualified version is T1, and for a binary operator @ with a left operand of a type whose cv-unqualified version is T1 and a right operand of a type whose cv-unqualified version is T2, four sets of candidate functions, designated member candidates, non-member candidates, built-in candidates, and rewritten candidates, are constructed as follows:

3.4.3 For the != operator ([expr.eq]), the rewritten candidates include all non-rewritten candidates for the expression x == y.

std::type_info and many more library types had their operator!= removed as part of P1614 - The Mothership has Landed.