Theorem simp1bi 919

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
simp1bi	|- ( ph -> ps )

Proof of Theorem simp1bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- ( ph <-> ( ps /\ ch /\ th ) )
2	1	biimpi 113	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp1d 916	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   <-> wb 98   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

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

This theorem is referenced by:  limord  4132  smores2  5909  smofvon2dm  5911  smofvon  5914  errel  6115  lincmb01cmp  8871  iccf1o  8872  elfznn0  8975  elfzouz  9008