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Theorem nfim1 1821
Description: A closed form of nfim 1769. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
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 nfim1.2 . . . . 5  |-  ( ph  ->  F/ x ps )
21nfrd 1743 . . . 4  |-  ( ph  ->  ( ps  ->  A. x ps ) )
32a2i 12 . . 3  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
4 nfim1.1 . . . 4  |-  F/ x ph
5419.21 1791 . . 3  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
63, 5sylibr 203 . 2  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
76nfi 1538 1  |-  F/ x
( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   F/wnf 1531
This theorem is referenced by:  sbco2d  2027
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1532
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