Theorem eqvisset 2740

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2736 and issetri 2739. (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 2733	. 2 |- x e. _V
2		eleq1 2233	. 2 |- ( x = A -> ( x e. _V <-> A e. _V ) )
3	1, 2	mpbii 147	1 |- ( x = A -> A e. _V )

Syntax hints:   -> wi 4   = wceq 1348   e. wcel 2141   _Vcvv 2730

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732

This theorem is referenced by:  elxp5  5099  xpsnen  6799  fival  6947