Theorem simp2bi 971

Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
3simp1bi.1	|- (ph <-> (ps /\ ch /\ th))

Assertion

Ref	Expression
simp2bi	|- (ph -> ch)

Proof of Theorem simp2bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- (ph <-> (ps /\ ch /\ th))
2	1	biimpi 186	. 2 |- (ph -> (ps /\ ch /\ th))
3	2	simp2d 968	1 |- (ph -> ch)

Syntax hints:   -> wi 4   <-> wb 176   /\ 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:  sfin111  4537  sbthlem3  6206