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Theorem nfeud 2157
Description: Deduction version of nfeu 2159. (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
StepHypRef Expression
1 nfeud.1 . 2  |-  F/ y
ph
2 nfeud.2 . . 3  |-  ( ph  ->  F/ x ps )
32adantr 451 . 2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
41, 3nfeud2 2155 1  |-  ( ph  ->  F/ x E! y ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   F/wnf 1531    = wceq 1623   E!weu 2143
This theorem is referenced by:  nfeu  2159
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-eu 2147
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