Theorem eqvisset 2609

Description: A class equal to a variable is a set. Note the absence of dv condition, contrary to isset 2605 and issetri 2608. (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 2604	. 2 |- x e. _V
2		eleq1 2141	. 2 |- ( x = A -> ( x e. _V <-> A e. _V ) )
3	1, 2	mpbii 146	1 |- ( x = A -> A e. _V )

Syntax hints:   -> wi 4   = wceq 1284   e. wcel 1433   _Vcvv 2601

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by:  elxp5  4829  xpsnen  6318