Theorem simp3bi 1014

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 1011	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 978

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 980

This theorem is referenced by:  limuni  4394  smores2  6290  ersym  6542  ertr  6545  fvixp  6698  fiintim  6923  eluzle  9534  ef01bndlem  11755  sin01bnd  11756  cos01bnd  11757  sin01gt0  11760  gznegcl  12363  gzcjcl  12364  gzaddcl  12365  gzmulcl  12366  gzabssqcl  12369  4sqlem4a  12379  ennnfonelemim  12415  subggrp  12963  srgdilem  13052  srgrz  13067  srglz  13068  ringdilem  13095  ringsrg  13124  reeff1oleme  13975  cosq14gt0  14035  cosq23lt0  14036  coseq0q4123  14037  coseq00topi  14038  coseq0negpitopi  14039  cosq34lt1  14053  cos02pilt1  14054  ioocosf1o  14057  2sqlem2  14233  2sqlem3  14235