How to implement not with if statement in Ember Handlebars?

You have many ways of doing that.

1. Use {{unless}}:

{{#unless isValid}}
  ...
{{else}}
  ...
{{/unless}}

2. Use inline-if helper:

{{#if (if isValid false true)}}
  ...
{{else}}
  ...
{{/if}}

3. Use ember-truth-helpers addon:

{{#if (not isValid)}}
  ...
{{else}}
  ...
{{/if}}

Simple answers for simple questions:

{{#unless isValid}}
{{/unless}}

Also keep in mind that you can insert an {{else}} in between an {{#if}} or {{#unless}} and the closing tag.