Theorem bj-issetiv 32863

Description: Version of bj-isseti 32864 with a dv condition on x , V. This proof uses only df-ex 1705, ax-gen 1722, ax-4 1737 and df-clel 2618 on top of propositional calculus. Prefer its use over bj-isseti 32864 when sufficient (in particular when V is substituted for _V). (Contributed by BJ, 14-Sep-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-issetiv.1	|- A e. V

Assertion

Ref	Expression
bj-issetiv	|- E. x x = A

Distinct variable groups:   x, A   x, V

Proof of Theorem bj-issetiv

Step	Hyp	Ref	Expression
1		bj-issetiv.1	. 2 |- A e. V
2		bj-elissetv 32861	. 2 |- ( A e. V -> E. x x = A )
3	1, 2	ax-mp 5	1 |- E. x x = A

Syntax hints:   = wceq 1483   E.wex 1704   e. wcel 1990

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-clel 2618

This theorem is referenced by:  bj-rexcom4bv  32871  bj-vtoclf  32908