Theorem simp2bi 1037

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 1034	1 |- ( ph -> ch )

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

This theorem depends on definitions:  df-bi 117  df-3an 1004

This theorem is referenced by:  0ellim  4489  smodm  6443  erdm  6698  ixpfn  6859  dif1en  7049  eluzelz  9743  elfz3nn0  10323  ef01bndlem  12282  sin01bnd  12283  cos01bnd  12284  sin01gt0  12288  bitsss  12471  gznegcl  12913  gzcjcl  12914  gzaddcl  12915  gzmulcl  12916  gzabssqcl  12919  4sqlem4a  12929  xpsff1o  13397  subgss  13726  rngmgp  13914  srgmgp  13946  ringmgp  13980  lmodring  14274  lmodprop2d  14327  reeff1oleme  15461  cosq14gt0  15521  cosq23lt0  15522  coseq0q4123  15523  coseq00topi  15524  coseq0negpitopi  15525  cosq34lt1  15539  cos02pilt1  15540  ioocosf1o  15543  gausslemma2dlem1a  15752  2sqlem2  15809  2sqlem3  15811