Theorem nf3or 1936

Description: If is not free in , , and , it is not free in . (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypotheses

Ref	Expression
nf.1
nf.2
nf.3

Assertion

Ref	Expression
nf3or

Proof of Theorem nf3or

Step	Hyp	Ref	Expression
1		df-3or 974	. 2
2		nf.1	. . . 4
3		nf.2	. . . 4
4	2, 3	nfor 1935	. . 3
5		nf.3	. . 3
6	4, 5	nfor 1935	. 2
7	1, 6	nfxfr 1645	1

Syntax hints:  \/wo 368  \/w3o 972  F/wnf 1616

This theorem is referenced by:  nfso  4811

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-or 370  df-3or 974  df-ex 1613  df-nf 1617