Theorem simp2bi 1016

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 1013	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 981

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 983

This theorem is referenced by:  0ellim  4458  smodm  6395  erdm  6648  ixpfn  6809  dif1en  6997  eluzelz  9687  elfz3nn0  10267  ef01bndlem  12152  sin01bnd  12153  cos01bnd  12154  sin01gt0  12158  bitsss  12341  gznegcl  12783  gzcjcl  12784  gzaddcl  12785  gzmulcl  12786  gzabssqcl  12789  4sqlem4a  12799  xpsff1o  13266  subgss  13595  rngmgp  13783  srgmgp  13815  ringmgp  13849  lmodring  14142  lmodprop2d  14195  reeff1oleme  15329  cosq14gt0  15389  cosq23lt0  15390  coseq0q4123  15391  coseq00topi  15392  coseq0negpitopi  15393  cosq34lt1  15407  cos02pilt1  15408  ioocosf1o  15411  gausslemma2dlem1a  15620  2sqlem2  15677  2sqlem3  15679