Theorem simp3bi 1045

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 1042	1 |- ( ph -> th )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  limuni  4543  smores2  6570  ersym  6824  ertr  6827  fvixp  6991  en2  7118  fiintim  7244  eluzle  9949  lincmble  10422  ef01bndlem  12547  sin01bnd  12548  cos01bnd  12549  sin01gt0  12553  gznegcl  13182  gzcjcl  13183  gzaddcl  13184  gzmulcl  13185  gzabssqcl  13188  4sqlem4a  13198  ennnfonelemim  13372  xpsff1o  13728  subggrp  14038  prdsbasprj  14288  srgdilem  14379  srgrz  14394  srglz  14395  ringdilem  14422  ringsrg  14458  subrngss  14616  lmodlema  14736  reeff1oleme  16015  cosq14gt0  16076  cosq23lt0  16077  coseq0q4123  16078  coseq00topi  16079  coseq0negpitopi  16080  cosq34lt1  16095  cos02pilt1  16096  ioocosf1o  16099  2sqlem2  16456  2sqlem3  16458