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  4442  smores2  6379  ersym  6631  ertr  6634  fvixp  6789  en2  6911  fiintim  7027  eluzle  9659  ef01bndlem  12038  sin01bnd  12039  cos01bnd  12040  sin01gt0  12044  gznegcl  12669  gzcjcl  12670  gzaddcl  12671  gzmulcl  12672  gzabssqcl  12675  4sqlem4a  12685  ennnfonelemim  12766  prdsbasprj  13085  xpsff1o  13152  subggrp  13484  srgdilem  13702  srgrz  13717  srglz  13718  ringdilem  13745  ringsrg  13780  subrngss  13933  lmodlema  14025  reeff1oleme  15215  cosq14gt0  15275  cosq23lt0  15276  coseq0q4123  15277  coseq00topi  15278  coseq0negpitopi  15279  cosq34lt1  15293  cos02pilt1  15294  ioocosf1o  15297  2sqlem2  15563  2sqlem3  15565