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Theorem nfmod 1933
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 1920 . 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 1660 . . 3  |-  ( ph  ->  F/ x E. y ps )
52, 3nfeud 1932 . . 3  |-  ( ph  ->  F/ x E! y ps )
64, 5nfimd 1493 . 2  |-  ( ph  ->  F/ x ( E. y ps  ->  E! y ps ) )
71, 6nfxfrd 1380 1  |-  ( ph  ->  F/ x E* y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1365   E.wex 1397   E!weu 1916   E*wmo 1917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920
This theorem is referenced by:  nfmo  1936
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