MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfor Unicode version

Theorem nfor 1782
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 359 . 2  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
2 nf.1 . . . 4  |-  F/ x ph
32nfn 1777 . . 3  |-  F/ x  -.  ph
4 nf.2 . . 3  |-  F/ x ps
53, 4nfim 1781 . 2  |-  F/ x
( -.  ph  ->  ps )
61, 5nfxfr 1560 1  |-  F/ x
( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357   F/wnf 1534
This theorem is referenced by:  nf3or  1785  nfun  3344  nfpr  3693  disjxun  4037  nfsum1  12179  nfsum  12180  nfcprod1  24132  nfcprod  24133  fdc1  26559  dvdsrabdioph  26994
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-nf 1535
  Copyright terms: Public domain W3C validator