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Theorem nfor 1585
Description: If  x is not free in  ph and  ps, it is not free in  ( ph  \/  ps ). (Contributed by Jim Kingdon, 11-Mar-2018.)
Hypotheses
Ref Expression
nfor.1  |-  F/ x ph
nfor.2  |-  F/ x ps
Assertion
Ref Expression
nfor  |-  F/ x
( ph  \/  ps )

Proof of Theorem nfor
StepHypRef Expression
1 nfor.1 . . . 4  |-  F/ x ph
21nfri 1530 . . 3  |-  ( ph  ->  A. x ph )
3 nfor.2 . . . 4  |-  F/ x ps
43nfri 1530 . . 3  |-  ( ps 
->  A. x ps )
52, 4hbor 1557 . 2  |-  ( (
ph  \/  ps )  ->  A. x ( ph  \/  ps ) )
65nfi 1473 1  |-  F/ x
( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:    \/ wo 709   F/wnf 1471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-gen 1460  ax-4 1521
This theorem depends on definitions:  df-bi 117  df-nf 1472
This theorem is referenced by:  nfdc  1670  nfun  3311  nfpr  3664  nfso  4327  nffrec  6436  indpi  7388  nfsum1  11473  nfsum  11474  nfcprod1  11671  nfcprod  11672  bj-findis  15395  isomninnlem  15444  trirec0  15458
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