Theorem nfnan 1825

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

Hypotheses

Ref	Expression
nfan.1	|- F/xph
nfan.2	|- F/xps

Assertion

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

Proof of Theorem nfnan

Step	Hyp	Ref	Expression
1		df-nan 1288	. 2 |- ((ph -/\ ps) <-> -. (ph /\ ps))
2		nfan.1	. . . 4 |- F/xph
3		nfan.2	. . . 4 |- F/xps
4	2, 3	nfan 1824	. . 3 |- F/x(ph /\ ps)
5	4	nfn 1793	. 2 |- F/x -. (ph /\ ps)
6	1, 5	nfxfr 1570	1 |- F/x(ph -/\ ps)

Syntax hints:  -. wn 3   /\ wa 358   -/\ wnan 1287   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-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfnin  3229