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  6569  ersym  6823  ertr  6826  fvixp  6989  en2  7116  fiintim  7242  eluzle  9950  lincmble  10423  ef01bndlem  12548  sin01bnd  12549  cos01bnd  12550  sin01gt0  12554  gznegcl  13183  gzcjcl  13184  gzaddcl  13185  gzmulcl  13186  gzabssqcl  13189  4sqlem4a  13199  ennnfonelemim  13373  xpsff1o  13729  subggrp  14039  prdsbasprj  14289  srgdilem  14380  srgrz  14395  srglz  14396  ringdilem  14423  ringsrg  14459  subrngss  14617  lmodlema  14737  reeff1oleme  15998  cosq14gt0  16059  cosq23lt0  16060  coseq0q4123  16061  coseq00topi  16062  coseq0negpitopi  16063  cosq34lt1  16078  cos02pilt1  16079  ioocosf1o  16082  2sqlem2  16439  2sqlem3  16441