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Theorem nfrimi 1459
Description: Moving an antecedent outside  F/. (Contributed by Jim Kingdon, 23-Mar-2018.)
Hypotheses
Ref Expression
nfrimi.1  |-  F/ x ph
nfrimi.2  |-  F/ x
( ph  ->  ps )
Assertion
Ref Expression
nfrimi  |-  ( ph  ->  F/ x ps )

Proof of Theorem nfrimi
StepHypRef Expression
1 nfrimi.1 . 2  |-  F/ x ph
2 nfrimi.2 . . . . 5  |-  F/ x
( ph  ->  ps )
32nfri 1453 . . . 4  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
41nfri 1453 . . . 4  |-  ( ph  ->  A. x ph )
5 ax-5 1377 . . . 4  |-  ( A. x ( ph  ->  ps )  ->  ( A. x ph  ->  A. x ps ) )
63, 4, 5syl2im 38 . . 3  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
76pm2.86i 97 . 2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
81, 7nfd 1457 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   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
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  hbsbd  1901
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