Theorem simp3bi 1038

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 1035	1 |- ( ph -> th )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 1002

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 1004

This theorem is referenced by:  limuni  4487  smores2  6446  ersym  6700  ertr  6703  fvixp  6858  en2  6981  fiintim  7104  eluzle  9746  ef01bndlem  12282  sin01bnd  12283  cos01bnd  12284  sin01gt0  12288  gznegcl  12913  gzcjcl  12914  gzaddcl  12915  gzmulcl  12916  gzabssqcl  12919  4sqlem4a  12929  ennnfonelemim  13010  prdsbasprj  13330  xpsff1o  13397  subggrp  13729  srgdilem  13947  srgrz  13962  srglz  13963  ringdilem  13990  ringsrg  14025  subrngss  14179  lmodlema  14271  reeff1oleme  15461  cosq14gt0  15521  cosq23lt0  15522  coseq0q4123  15523  coseq00topi  15524  coseq0negpitopi  15525  cosq34lt1  15539  cos02pilt1  15540  ioocosf1o  15543  2sqlem2  15809  2sqlem3  15811