Theorem 3expb 1152

Description: Exportation from triple to double conjunction. (Contributed by NM, 20-Aug-1995.)

Hypothesis

Ref	Expression
3exp.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3expb	|- ((ph /\ (ps /\ ch)) -> th)

Proof of Theorem 3expb

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 |- ((ph /\ ps /\ ch) -> th)
2	1	3exp 1150	. 2 |- (ph -> (ps -> (ch -> th)))
3	2	imp32 422	1 |- ((ph /\ (ps /\ ch)) -> th)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  3adant3r1  1160  3adant3r2  1161  3adant3r3  1162  3adant1l  1174  3adant1r  1175  mp3an1  1264  sfin112  4530  fnfco  5238  fununiq  5518  mpt2eq3dva  5670  peano4nc  6151