Theorem nf3and 1461

Description: Deduction form of bound-variable hypothesis builder nf3an 1458. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.)

Hypotheses

Ref	Expression
nfand.1	|- ( ph -> F/ x ps )
nfand.2	|- ( ph -> F/ x ch )
nfand.3	|- ( ph -> F/ x th )

Assertion

Ref	Expression
nf3and	|- ( ph -> F/ x ( ps /\ ch /\ th ) )

Proof of Theorem nf3and

Step	Hyp	Ref	Expression
1		df-3an 887	. 2 |- ( ( ps /\ ch /\ th ) <-> ( ( ps /\ ch ) /\ th ) )
2		nfand.1	. . . 4 |- ( ph -> F/ x ps )
3		nfand.2	. . . 4 |- ( ph -> F/ x ch )
4	2, 3	nfand 1460	. . 3 |- ( ph -> F/ x ( ps /\ ch ) )
5		nfand.3	. . 3 |- ( ph -> F/ x th )
6	4, 5	nfand 1460	. 2 |- ( ph -> F/ x ( ( ps /\ ch ) /\ th ) )
7	1, 6	nfxfrd 1364	1 |- ( ph -> F/ x ( ps /\ ch /\ th ) )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885   F/wnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338

This theorem depends on definitions:  df-bi 110  df-3an 887  df-nf 1350

This theorem is referenced by: (None)