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Theorem nf3or 1860
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 938 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
2 nf.1 . . . 4  |-  F/ x ph
3 nf.2 . . . 4  |-  F/ x ps
42, 3nfor 1859 . . 3  |-  F/ x
( ph  \/  ps )
5 nf.3 . . 3  |-  F/ x ch
64, 5nfor 1859 . 2  |-  F/ x
( ( ph  \/  ps )  \/  ch )
71, 6nfxfr 1580 1  |-  F/ x
( ph  \/  ps  \/  ch )
Colors of variables: wff set class
Syntax hints:    \/ wo 359    \/ w3o 936   F/wnf 1554
This theorem is referenced by:  nfso  4511
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-or 361  df-3or 938  df-tru 1329  df-ex 1552  df-nf 1555
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