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Theorem nfmod2 2277
Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfmod2.1  |-  F/ y
ph
nfmod2.2  |-  ( (
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 2268 . 2  |-  ( E* y ps  <->  ( E. y ps  ->  E! y ps ) )
2 nfmod2.1 . . . 4  |-  F/ y
ph
3 nfmod2.2 . . . 4  |-  ( (
ph  /\  -.  A. x  x  =  y )  ->  F/ x ps )
42, 3nfexd2 2127 . . 3  |-  ( ph  ->  F/ x E. y ps )
52, 3nfeud2 2276 . . 3  |-  ( ph  ->  F/ x E! y ps )
64, 5nfimd 1972 . 2  |-  ( ph  ->  F/ x ( E. y ps  ->  E! y ps ) )
71, 6nfxfrd 1693 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 370   A.wal 1435   E.wex 1659   F/wnf 1663   E!weu 2263   E*wmo 2264
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052
This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-eu 2267  df-mo 2268
This theorem is referenced by:  nfmod  2279  nfrmod  3000  nfrmo  3002  nfdisj  4400
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