Theorem simp1bi 1043

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
simp1bi	|- ( ph -> ps )

Proof of Theorem simp1bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- ( ph <-> ( ps /\ ch /\ th ) )
2	1	biimpi 120	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp1d 1040	1 |- ( ph -> ps )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  limord  4542  smores2  6570  smofvon2dm  6572  smofvon  6575  errel  6821  lincmb01cmp  10421  lincmble  10422  iccf1o  10423  elfznn0  10537  elfzouz  10574  ef01bndlem  12547  sin01bnd  12548  cos01bnd  12549  sin01gt0  12553  cos01gt0  12554  sin02gt0  12555  eulerthlema  13036  modprm0  13061  gzcn  13179  ballotfilemscr  13319  ballotfilemrinv0  13333  subgbas  14039  subgrcl  14040  rngabl  14340  srgcmn  14376  ringgrp  14411  subrngrcl  14619  lmodgrp  14738  coseq00topi  16079  coseq0negpitopi  16080  cosq34lt1  16095  cos11  16098  clwwlkbp  16858  clwwlksswrd  16860  nconstwlpolemgt0  17338