Theorem simp3d 969

Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005.)

Hypothesis

Ref	Expression
3simp1d.1	|- (ph -> (ps /\ ch /\ th))

Assertion

Ref	Expression
simp3d	|- (ph -> th)

Proof of Theorem simp3d

Step	Hyp	Ref	Expression
1		3simp1d.1	. 2 |- (ph -> (ps /\ ch /\ th))
2		simp3 957	. 2 |- ((ps /\ ch /\ th) -> th)
3	1, 2	syl 15	1 |- (ph -> th)

Syntax hints:   -> wi 4   /\ 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:  simp3bi  972