Theorem nfeu1

Description: Bound-variable hypothesis builder for uniqueness. See also nfeu1ALT . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016)

	Ref	Expression
Assertion	nfeu1	|- F/ x E! x ph

Proof

Step	Hyp	Ref	Expression
1		eu6	|- ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2		nfa1	|- F/ x A. x ( ph <-> x = y )
3	2	nfex	|- F/ x E. y A. x ( ph <-> x = y )
4	1 3	nfxfr	|- F/ x E! x ph