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Theorem nfim1 1833
Description: A closed form of nfim 1781. (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 1755 . . . 4  |-  ( ph  ->  ( ps  ->  A. x ps ) )
32a2i 12 . . 3  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
4 nfim1.1 . . . 4  |-  F/ x ph
5419.21 1803 . . 3  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
63, 5sylibr 203 . 2  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
76nfi 1541 1  |-  F/ x
( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   F/wnf 1534
This theorem is referenced by:  sbco2d  2040  sbco2dwAUX7  29560  sbco2dOLD7  29707
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1535
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