Theorem simp3bi 1017

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 1014	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 981

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 983

This theorem is referenced by:  limuni  4461  smores2  6403  ersym  6655  ertr  6658  fvixp  6813  en2  6936  fiintim  7054  eluzle  9695  ef01bndlem  12182  sin01bnd  12183  cos01bnd  12184  sin01gt0  12188  gznegcl  12813  gzcjcl  12814  gzaddcl  12815  gzmulcl  12816  gzabssqcl  12819  4sqlem4a  12829  ennnfonelemim  12910  prdsbasprj  13229  xpsff1o  13296  subggrp  13628  srgdilem  13846  srgrz  13861  srglz  13862  ringdilem  13889  ringsrg  13924  subrngss  14077  lmodlema  14169  reeff1oleme  15359  cosq14gt0  15419  cosq23lt0  15420  coseq0q4123  15421  coseq00topi  15422  coseq0negpitopi  15423  cosq34lt1  15437  cos02pilt1  15438  ioocosf1o  15441  2sqlem2  15707  2sqlem3  15709