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  6460  ersym  6714  ertr  6717  fvixp  6872  en2  6998  fiintim  7123  eluzle  9768  ef01bndlem  12318  sin01bnd  12319  cos01bnd  12320  sin01gt0  12324  gznegcl  12949  gzcjcl  12950  gzaddcl  12951  gzmulcl  12952  gzabssqcl  12955  4sqlem4a  12965  ennnfonelemim  13046  prdsbasprj  13366  xpsff1o  13433  subggrp  13765  srgdilem  13984  srgrz  13999  srglz  14000  ringdilem  14027  ringsrg  14062  subrngss  14216  lmodlema  14308  reeff1oleme  15498  cosq14gt0  15558  cosq23lt0  15559  coseq0q4123  15560  coseq00topi  15561  coseq0negpitopi  15562  cosq34lt1  15576  cos02pilt1  15577  ioocosf1o  15580  2sqlem2  15846  2sqlem3  15848