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Theorem nfmod2 2244
Description: Bound-variable hypothesis builder for uniqueness. (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 2236 . 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 1999 . . 3  |-  ( ph  ->  F/ x E. y ps )
52, 3nfeud2 2243 . . 3  |-  ( ph  ->  F/ x E! y ps )
64, 5nfimd 1817 . 2  |-  ( ph  ->  F/ x ( E. y ps  ->  E! y ps ) )
71, 6nfxfrd 1577 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 359   A.wal 1546   E.wex 1547   F/wnf 1550   E!weu 2231   E*wmo 2232
This theorem is referenced by:  nfmod  2246  nfrmod  2817  nfrmo  2819  nfdisj  4128
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-eu 2235  df-mo 2236
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