Theorem bj-issetw

Description: The closest one can get to isset without using ax-ext . See also vexw . Note that the only disjoint variable condition is between y and A . From there, one can prove isset using eleq2i (which requires ax-ext and df-cleq ). (Contributed by BJ, 29-Apr-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-issetw.1	|- ph
Assertion	bj-issetw	|- ( A e. { x | ph } <-> E. y y = A )

Proof

Step	Hyp	Ref	Expression
1		bj-issetw.1	|- ph
2		bj-issetwt	|- ( A. x ph -> ( A e. { x | ph } <-> E. y y = A ) )
3	2 1	mpg	|- ( A e. { x | ph } <-> E. y y = A )