Theorem bj-isseti

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

	Ref	Expression
Hypothesis	bj-isseti.1	|- A e. V
Assertion	bj-isseti	|- E. x x = A

Proof

Step	Hyp	Ref	Expression
1		bj-isseti.1	|- A e. V
2		bj-elisset	|- ( A e. V -> E. x x = A )
3	1 2	ax-mp	|- E. x x = A