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Theorem nfmod 2171
Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfeud.1  |-  F/ y
ph
nfeud.2  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfmod  |-  ( ph  ->  F/ x E* y ps )

Proof of Theorem nfmod
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, 3nfmod2 2169 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   F/wnf 1534    = wceq 1632   E*wmo 2157
This theorem is referenced by:  nfmo  2173
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160  df-mo 2161
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