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Theorem nfim1 1504
Description: A closed form of nfim 1505. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
nfim1.1  |-  F/ x ph
nfim1.2  |-  ( ph  ->  F/ x ps )
Assertion
Ref Expression
nfim1  |-  F/ x
( ph  ->  ps )

Proof of Theorem nfim1
StepHypRef Expression
1 nfim1.1 . . . 4  |-  F/ x ph
21nfri 1453 . . 3  |-  ( ph  ->  A. x ph )
3 nfim1.2 . . . 4  |-  ( ph  ->  F/ x ps )
43nfrd 1454 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
52, 4hbim1 1503 . 2  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
65nfi 1392 1  |-  F/ x
( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1390
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-5 1377  ax-gen 1379  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  nfim  1505  cbv1  1673  hbsbd  1900
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