Theorem nfeud 2484

Description: Deduction version of nfeu 2486. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 7-Oct-2016.)

Hypotheses

Ref	Expression
nfeud.1	|- F/ y ph
nfeud.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfeud	|- ( ph -> F/ x E! y ps )

Proof of Theorem nfeud

Step	Hyp	Ref	Expression
1		nfeud.1	. 2 |- F/ y ph
2		nfeud.2	. . 3 |- ( ph -> F/ x ps )
3	2	adantr 481	. 2 |- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4	1, 3	nfeud2 2482	1 |- ( ph -> F/ x E! y ps )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   F/wnf 1708   E!weu 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-eu 2474

This theorem is referenced by:  nfeu  2486