Theorem nf3an 1827

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
nfan.1	|- F/xph
nfan.2	|- F/xps
nfan.3	|- F/xch

Assertion

Ref	Expression
nf3an	|- F/x(ph /\ ps /\ ch)

Proof of Theorem nf3an

Step	Hyp	Ref	Expression
1		df-3an 936	. 2 |- ((ph /\ ps /\ ch) <-> ((ph /\ ps) /\ ch))
2		nfan.1	. . . 4 |- F/xph
3		nfan.2	. . . 4 |- F/xps
4	2, 3	nfan 1824	. . 3 |- F/x(ph /\ ps)
5		nfan.3	. . 3 |- F/xch
6	4, 5	nfan 1824	. 2 |- F/x((ph /\ ps) /\ ch)
7	1, 6	nfxfr 1570	1 |- F/x(ph /\ ps /\ ch)

Syntax hints:   /\ wa 358   /\ w3a 934   F/wnf 1544

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  hb3an  1830  vtocl3gaf  2923  mob  3018