Theorem eqvisset 2722

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2718 and issetri 2721. (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 2715	. 2 |- x e. _V
2		eleq1 2220	. 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 1335   e. wcel 2128   _Vcvv 2712

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 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-v 2714

This theorem is referenced by:  elxp5  5074  xpsnen  6766  fival  6914