Theorem simp2bi 1044

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 1041	1 |- ( ph -> ch )

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  ax-ia2 107

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

This theorem is used by:  0ellim  4545  smodm  6567  erdm  6822  ixpfn  6992  dif1en  7189  eluzelz  9946  lincmble  10422  elfz3nn0  10538  ef01bndlem  12547  sin01bnd  12548  cos01bnd  12549  sin01gt0  12553  bitsss  12736  gznegcl  13182  gzcjcl  13183  gzaddcl  13184  gzmulcl  13185  gzabssqcl  13188  4sqlem4a  13198  xpsff1o  13728  subgss  14035  rngmgp  14341  srgmgp  14378  ringmgp  14412  lmodring  14739  lmodprop2d  14793  reeff1oleme  16015  cosq14gt0  16076  cosq23lt0  16077  coseq0q4123  16078  coseq00topi  16079  coseq0negpitopi  16080  cosq34lt1  16095  cos02pilt1  16096  ioocosf1o  16099  gausslemma2dlem1a  16399  2sqlem2  16456  2sqlem3  16458