Theorem simp2bi 954

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 118	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp2d 951	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   <-> wb 103   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  0ellim  4153  smodm  5929  erdm  6139  dif1en  6364  eluzelz  8628  elfz3nn0  9131