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  6457  erdm  6712  ixpfn  6873  dif1en  7068  eluzelz  9765  elfz3nn0  10350  ef01bndlem  12318  sin01bnd  12319  cos01bnd  12320  sin01gt0  12324  bitsss  12507  gznegcl  12949  gzcjcl  12950  gzaddcl  12951  gzmulcl  12952  gzabssqcl  12955  4sqlem4a  12965  xpsff1o  13433  subgss  13762  rngmgp  13951  srgmgp  13983  ringmgp  14017  lmodring  14311  lmodprop2d  14364  reeff1oleme  15498  cosq14gt0  15558  cosq23lt0  15559  coseq0q4123  15560  coseq00topi  15561  coseq0negpitopi  15562  cosq34lt1  15576  cos02pilt1  15577  ioocosf1o  15580  gausslemma2dlem1a  15789  2sqlem2  15846  2sqlem3  15848