Theorem issetf

Description: A version of isset that does not require x and A to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011) (Revised by Mario Carneiro, 10-Oct-2016)

	Ref	Expression
Hypothesis	issetf.1	|- F/_ x A
Assertion	issetf	|- ( A e. _V <-> E. x x = A )

Proof

Step	Hyp	Ref	Expression
1		issetf.1	|- F/_ x A
2		isset	|- ( A e. _V <-> E. y y = A )
3	1	nfeq2	|- F/ x y = A
4		nfv	|- F/ y x = A
5		eqeq1	|- ( y = x -> ( y = A <-> x = A ) )
6	3 4 5	cbvexv1	|- ( E. y y = A <-> E. x x = A )
7	2 6	bitri	|- ( A e. _V <-> E. x x = A )