Theorem eqvisset 2787

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2783 and issetri 2786. (Contributed by BJ, 27-Apr-2019.)

Assertion

Ref	Expression
eqvisset	|- ( x = A -> A e. _V )

Proof of Theorem eqvisset

Step	Hyp	Ref	Expression
1		vex 2779	. 2 |- x e. _V
2		eleq1 2270	. 2 |- ( x = A -> ( x e. _V <-> A e. _V ) )
3	1, 2	mpbii 148	1 |- ( x = A -> A e. _V )

Syntax hints:   -> wi 4   = wceq 1373   e. wcel 2178   _Vcvv 2776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-v 2778

This theorem is referenced by:  elxp5  5190  xpsnen  6941  fival  7098