Metamath Proof Explorer


Theorem nfeu1ALT

Description: Alternate version of nfeu1 with a shorter proof but using ax-12 . Bound-variable hypothesis builder for uniqueness. See also nfeu1 . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion nfeu1ALT
|- F/ x E! x ph

Proof

Step Hyp Ref Expression
1 eu6
 |-  ( E! x ph <-> E. y A. x ( ph <-> x = y ) )
2 nfexa2
 |-  F/ x E. y A. x ( ph <-> x = y )
3 1 2 nfxfr
 |-  F/ x E! x ph