Theorem simp3bi 1016

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 120	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp3d 1013	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  limuni  4431  smores2  6352  ersym  6604  ertr  6607  fvixp  6762  fiintim  6992  eluzle  9613  ef01bndlem  11921  sin01bnd  11922  cos01bnd  11923  sin01gt0  11927  gznegcl  12544  gzcjcl  12545  gzaddcl  12546  gzmulcl  12547  gzabssqcl  12550  4sqlem4a  12560  ennnfonelemim  12641  xpsff1o  12992  subggrp  13307  srgdilem  13525  srgrz  13540  srglz  13541  ringdilem  13568  ringsrg  13603  subrngss  13756  lmodlema  13848  reeff1oleme  15008  cosq14gt0  15068  cosq23lt0  15069  coseq0q4123  15070  coseq00topi  15071  coseq0negpitopi  15072  cosq34lt1  15086  cos02pilt1  15087  ioocosf1o  15090  2sqlem2  15356  2sqlem3  15358