Theorem nf3or 1835

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

Step	Hyp	Ref	Expression
1		df-3or 1038	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
2		nf.1	. . . 4 |- F/ x ph
3		nf.2	. . . 4 |- F/ x ps
4	2, 3	nfor 1834	. . 3 |- F/ x ( ph \/ ps )
5		nf.3	. . 3 |- F/ x ch
6	4, 5	nfor 1834	. 2 |- F/ x ( ( ph \/ ps ) \/ ch )
7	1, 6	nfxfr 1779	1 |- F/ x ( ph \/ ps \/ ch )

Syntax hints:   \/ wo 383   \/ w3o 1036   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-3or 1038  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfso  5041