Theorem nfor 1834

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

Step	Hyp	Ref	Expression
1		df-or 385	. 2 |- ( ( ph \/ ps ) <-> ( -. ph -> ps ) )
2		nf.1	. . . 4 |- F/ x ph
3	2	nfn 1784	. . 3 |- F/ x -. ph
4		nf.2	. . 3 |- F/ x ps
5	3, 4	nfim 1825	. 2 |- F/ x ( -. ph -> ps )
6	1, 5	nfxfr 1779	1 |- F/ x ( ph \/ ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  nf3or  1835  axi12  2600  nfun  3769  nfpr  4232  rabsnifsb  4257  disjxun  4651  fsuppmapnn0fiubex  12792  nfsum1  14420  nfsum  14421  nfcprod1  14640  nfcprod  14641  fdc1  33542  dvdsrabdioph  37374  disjinfi  39380  iundjiun  40677