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Theorem nfmod 1965
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 df-mo 1952 . 2  |-  ( E* y ps  <->  ( E. y ps  ->  E! y ps ) )
2 nfeud.1 . . . 4  |-  F/ y
ph
3 nfeud.2 . . . 4  |-  ( ph  ->  F/ x ps )
42, 3nfexd 1691 . . 3  |-  ( ph  ->  F/ x E. y ps )
52, 3nfeud 1964 . . 3  |-  ( ph  ->  F/ x E! y ps )
64, 5nfimd 1522 . 2  |-  ( ph  ->  F/ x ( E. y ps  ->  E! y ps ) )
71, 6nfxfrd 1409 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1394   E.wex 1426   E!weu 1948   E*wmo 1949
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  nfmo  1968
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