Theorem eqvisset 2782

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2778 and issetri 2781. (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 2775	. 2 |- x e. _V
2		eleq1 2268	. 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 2176   _Vcvv 2772

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774

This theorem is referenced by:  elxp5  5171  xpsnen  6916  fival  7072