Theorem simp3bi 1040

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 1037	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 1004

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 1006

This theorem is referenced by:  limuni  4493  smores2  6459  ersym  6713  ertr  6716  fvixp  6871  en2  6997  fiintim  7122  eluzle  9767  ef01bndlem  12316  sin01bnd  12317  cos01bnd  12318  sin01gt0  12322  gznegcl  12947  gzcjcl  12948  gzaddcl  12949  gzmulcl  12950  gzabssqcl  12953  4sqlem4a  12963  ennnfonelemim  13044  prdsbasprj  13364  xpsff1o  13431  subggrp  13763  srgdilem  13981  srgrz  13996  srglz  13997  ringdilem  14024  ringsrg  14059  subrngss  14213  lmodlema  14305  reeff1oleme  15495  cosq14gt0  15555  cosq23lt0  15556  coseq0q4123  15557  coseq00topi  15558  coseq0negpitopi  15559  cosq34lt1  15573  cos02pilt1  15574  ioocosf1o  15577  2sqlem2  15843  2sqlem3  15845