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Because I haven't used this rule.
One thing I want to confirm about this change is:

BinaryExpression encompasses much more than just equality checks: https://github.com/estree/estree/blob/master/es5.md#binaryexpression

enum BinaryOperator {
    "==" | "!=" | "===" | "!=="
         | "<" | "<=" | ">" | ">="
         | "<<" | ">>" | ">>>"
         | "+" | "-" | "*" | "/" | "%"
         | "|" | "^" | "&" | "in"
         | "instanceof"
}

Are we okay with opening this rule up to "ignore" all of these operators?
If yes, then LGTM. If no, then please add a check for the operator.

@bradzacher

if (x.y) {}
    ^^^
    MemberExpression -> Parent `IfStatement`

The issue in this case that if we check MemberExpression (!==, ==, etc). a parent doesn't equal to IfStatement, parent equals to BinaryExpression. For that reason I added new type to switch statement to ignore all Member Expressions which have parentBinaryExpressions. On need to check Parent for BinaryExpression not to MemberExpression?

if (x.y !== 1) {}
    ^^^
    MemberExpression -> Parent `BinaryExpression` -> Parent `IfStatement`

Sorry - i meant rather than just saying "having a parent of type BinaryExpression is fine", I was meaning - do we want to limit the scope a little bit.
I.e. "having a parent of BinaryExpression is fine, as long as
['==', '!=', '===', '!==', 'instanceof'].includes(parentBinaryExpression.operator)"

I think this is fine as is though. I don't think any of the other binary operators should cause problems.

@bradzacher oke.

Codecov Report

Merging #914 into master will increase coverage by <.01%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master     #914      +/-   ##
==========================================
+ Coverage   94.07%   94.08%   +<.01%     
==========================================
  Files         113      113              
  Lines        4915     4916       +1     
  Branches     1369     1369              
==========================================
+ Hits         4624     4625       +1     
  Misses        165      165              
  Partials      126      126