Theorem eqvisset 2651

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2647 and issetri 2650. (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 2644	. 2 |- x e. _V
2		eleq1 2162	. 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 1299   e. wcel 1448   _Vcvv 2641

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-ext 2082

This theorem depends on definitions:  df-bi 116  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-v 2643

This theorem is referenced by:  elxp5  4963  xpsnen  6644