Theorem simp3bi 960

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
simp3bi	|- ( ph -> th )

Proof of Theorem simp3bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- ( ph <-> ( ps /\ ch /\ th ) )
2	1	biimpi 118	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp3d 957	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 103   /\ w3a 924

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 926

This theorem is referenced by:  limuni  4223  smores2  6059  ersym  6302  ertr  6305  fiintim  6637  eluzle  9029  ef01bndlem  11043  sin01bnd  11044  cos01bnd  11045  sin01gt0  11048