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Theorem nfor 1873
Description: If  x is not free in  ph and  ps, it is not free in  ( ph  \/  ps ). (Contributed by NM, 5-Aug-1993.) (Revised 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 370 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
2 nf.1 . . . 4  |-  F/ x ph
32nfn 1840 . . 3  |-  F/ x  -.  ph
4 nf.2 . . 3  |-  F/ x ps
53, 4nfim 1858 . 2  |-  F/ x
( -.  ph  ->  ps )
61, 5nfxfr 1616 1  |-  F/ x
( ph  \/  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368   F/wnf 1590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-or 370  df-ex 1588  df-nf 1591
This theorem is referenced by:  nf3or  1874  axi12  2430  nfun  3621  nfpr  4032  rabsnifsb  4052  disjxun  4399  nfsum1  13286  nfsum  13287  nfcprod1  27568  nfcprod  27569  fdc1  28791  dvdsrabdioph  29297  fsuppmapnn0fiubex  30949
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