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Theorem nfor 1860
Description: If  x is not free in  ph and  ps, it is not free in  ( ph  \/  ps ). (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nf.1  |-  F/ x ph
nf.2  |-  F/ x ps
Assertion
Ref Expression
nfor  |-  F/ x
( ph  \/  ps )

Proof of Theorem nfor
StepHypRef Expression
1 df-or 361 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
2 nf.1 . . . 4  |-  F/ x ph
32nfn 1813 . . 3  |-  F/ x  -.  ph
4 nf.2 . . 3  |-  F/ x ps
53, 4nfim 1834 . 2  |-  F/ x
( -.  ph  ->  ps )
61, 5nfxfr 1580 1  |-  F/ x
( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 359   F/wnf 1554
This theorem is referenced by:  nf3or  1861  axi12  2421  nfun  3489  nfpr  3879  disjxun  4235  nfsum1  12515  nfsum  12516  nfcprod1  25267  nfcprod  25268  fdc1  26488  dvdsrabdioph  26908
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-11 1763
This theorem depends on definitions:  df-bi 179  df-or 361  df-tru 1329  df-ex 1552  df-nf 1555
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