Theorem simp2bi 1039

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
simp2bi	|- ( ph -> ch )

Proof of Theorem simp2bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- ( ph <-> ( ps /\ ch /\ th ) )
2	1	biimpi 120	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp2d 1036	1 |- ( ph -> ch )

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

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  0ellim  4495  smodm  6456  erdm  6711  ixpfn  6872  dif1en  7067  eluzelz  9764  elfz3nn0  10349  ef01bndlem  12316  sin01bnd  12317  cos01bnd  12318  sin01gt0  12322  bitsss  12505  gznegcl  12947  gzcjcl  12948  gzaddcl  12949  gzmulcl  12950  gzabssqcl  12953  4sqlem4a  12963  xpsff1o  13431  subgss  13760  rngmgp  13948  srgmgp  13980  ringmgp  14014  lmodring  14308  lmodprop2d  14361  reeff1oleme  15495  cosq14gt0  15555  cosq23lt0  15556  coseq0q4123  15557  coseq00topi  15558  coseq0negpitopi  15559  cosq34lt1  15573  cos02pilt1  15574  ioocosf1o  15577  gausslemma2dlem1a  15786  2sqlem2  15843  2sqlem3  15845