Theorem eqvisset 2770

Description: A class equal to a variable is a set. Note the absence of disjoint variable condition, contrary to isset 2766 and issetri 2769. (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 2763	. 2 |- x e. _V
2		eleq1 2256	. 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 1364   e. wcel 2164   _Vcvv 2760

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762

This theorem is referenced by:  elxp5  5155  xpsnen  6877  fival  7031