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Theorem nfmod2 2293
Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfeud2.1  |-  F/ y
ph
nfeud2.2  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
Assertion
Ref Expression
nfmod2  |-  ( ph  ->  F/ x E* y ps )

Proof of Theorem nfmod2
StepHypRef Expression
1 df-mo 2285 . 2  |-  ( E* y ps  <->  ( E. y ps  ->  E! y ps ) )
2 nfeud2.1 . . . 4  |-  F/ y
ph
3 nfeud2.2 . . . 4  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
42, 3nfexd2 2061 . . 3  |-  ( ph  ->  F/ x E. y ps )
52, 3nfeud2 2292 . . 3  |-  ( ph  ->  F/ x E! y ps )
64, 5nfimd 1827 . 2  |-  ( ph  ->  F/ x ( E. y ps  ->  E! y ps ) )
71, 6nfxfrd 1580 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359   A.wal 1549   E.wex 1550   F/wnf 1553   E!weu 2280   E*wmo 2281
This theorem is referenced by:  nfmod  2295  nfrmod  2873  nfrmo  2875  nfdisj  4186
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-eu 2284  df-mo 2285
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