Theorem nf3or 1837

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/xph
nf.2	|- F/xps
nf.3	|- F/xch

Assertion

Ref	Expression
nf3or	|- F/x(ph \/ ps \/ ch)

Proof of Theorem nf3or

Step	Hyp	Ref	Expression
1		df-3or 935	. 2 |- ((ph \/ ps \/ ch) <-> ((ph \/ ps) \/ ch))
2		nf.1	. . . 4 |- F/xph
3		nf.2	. . . 4 |- F/xps
4	2, 3	nfor 1836	. . 3 |- F/x(ph \/ ps)
5		nf.3	. . 3 |- F/xch
6	4, 5	nfor 1836	. 2 |- F/x((ph \/ ps) \/ ch)
7	1, 6	nfxfr 1570	1 |- F/x(ph \/ ps \/ ch)

Syntax hints:   \/ wo 357   \/ w3o 933   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-or 359  df-3or 935  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by: (None)