Theorem eqvisset 2696

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2692 and issetri 2695. (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 2689	. 2 |- x e. _V
2		eleq1 2202	. 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 1331   e. wcel 1480   _Vcvv 2686

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688

This theorem is referenced by:  elxp5  5027  xpsnen  6715  fival  6858