Theorem nfnan 1929

Description: If is not free in and , then it is not free in . (Contributed by Scott Fenton, 2-Jan-2018.)

Hypotheses

Ref	Expression
nfan.1
nfan.2

Assertion

Ref	Expression
nfnan

Proof of Theorem nfnan

Step	Hyp	Ref	Expression
1		df-nan 1344	. 2
2		nfan.1	. . . 4
3		nfan.2	. . . 4
4	2, 3	nfan 1928	. . 3
5	4	nfn 1901	. 2
6	1, 5	nfxfr 1645	1

Syntax hints:  -.wn 3  /\wa 369  -/\wnan 1343  F/wnf 1616

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-an 371  df-nan 1344  df-ex 1613  df-nf 1617