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Theorem nf3or 1993
Description: If  x is not free in  ph,  ps, and  ch, it is not free in  ( ph  \/  ps  \/  ch ). (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nf.1  |-  F/ x ph
nf.2  |-  F/ x ps
nf.3  |-  F/ x ch
Assertion
Ref Expression
nf3or  |-  F/ x
( ph  \/  ps  \/  ch )

Proof of Theorem nf3or
StepHypRef Expression
1 df-3or 984 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 nf.1 . . . 4  |-  F/ x ph
3 nf.2 . . . 4  |-  F/ x ps
42, 3nfor 1992 . . 3  |-  F/ x
( ph  \/  ps )
5 nf.3 . . 3  |-  F/ x ch
64, 5nfor 1992 . 2  |-  F/ x
( ( ph  \/  ps )  \/  ch )
71, 6nfxfr 1693 1  |-  F/ x
( ph  \/  ps  \/  ch )
Colors of variables: wff setvar class
Syntax hints:    \/ wo 370    \/ w3o 982   F/wnf 1664
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-or 372  df-3or 984  df-ex 1661  df-nf 1665
This theorem is referenced by:  nfso  4778
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