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Theorem nfor 1858
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 360 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
2 nf.1 . . . 4  |-  F/ x ph
32nfn 1811 . . 3  |-  F/ x  -.  ph
4 nf.2 . . 3  |-  F/ x ps
53, 4nfim 1832 . 2  |-  F/ x
( -.  ph  ->  ps )
61, 5nfxfr 1579 1  |-  F/ x
( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 358   F/wnf 1553
This theorem is referenced by:  nf3or  1859  axi12  2414  nfun  3495  nfpr  3847  disjxun  4202  nfsum1  12472  nfsum  12473  nfcprod1  25225  nfcprod  25226  fdc1  26387  dvdsrabdioph  26807
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-or 360  df-tru 1328  df-ex 1551  df-nf 1554
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