Theorem bj-isseti 32864

Description: Remove from isseti 3209 dependency on ax-ext 2602 (and on df-cleq 2615 and df-v 3202). This proof uses only df-clab 2609 and df-clel 2618 on top of first-order logic. It only uses ax-12 2047 among the auxiliary logical axioms. The hypothesis uses V instead of _V for extra generality. This is indeed more general as long as elex 3212 is not available. Use bj-issetiv 32863 instead when sufficient (in particular when V is substituted for _V). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.)

Hypothesis

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

Assertion

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

Distinct variable group:   x, A

Allowed substitution hint:   V( x)

Proof of Theorem bj-isseti

Step	Hyp	Ref	Expression
1		bj-isseti.1	. 2 |- A e. V
2		bj-elisset 32862	. 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  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881  df-clab 2609  df-clel 2618

This theorem is referenced by:  bj-rexcom4b  32872