Theorem nfnan 1830

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/ x ph
nfan.2	|- F/ x ps

Assertion

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

Proof of Theorem nfnan

Step	Hyp	Ref	Expression
1		df-nan 1448	. 2 |- ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
2		nfan.1	. . . 4 |- F/ x ph
3		nfan.2	. . . 4 |- F/ x ps
4	2, 3	nfan 1828	. . 3 |- F/ x ( ph /\ ps )
5	4	nfn 1784	. 2 |- F/ x -. ( ph /\ ps )
6	1, 5	nfxfr 1779	1 |- F/ x ( ph -/\ ps )

Syntax hints:   -. wn 3   /\ wa 384   -/\ wnan 1447   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-nan 1448  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)