Theorem simp2bi 1013

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 1010	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   <-> wb 105   /\ w3a 978

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 980

This theorem is referenced by:  0ellim  4397  smodm  6289  erdm  6542  ixpfn  6701  dif1en  6876  eluzelz  9533  elfz3nn0  10110  ef01bndlem  11757  sin01bnd  11758  cos01bnd  11759  sin01gt0  11762  gznegcl  12365  gzcjcl  12366  gzaddcl  12367  gzmulcl  12368  gzabssqcl  12371  4sqlem4a  12381  subgss  12965  srgmgp  13082  ringmgp  13116  reeff1oleme  14064  cosq14gt0  14124  cosq23lt0  14125  coseq0q4123  14126  coseq00topi  14127  coseq0negpitopi  14128  cosq34lt1  14142  cos02pilt1  14143  ioocosf1o  14146  2sqlem2  14322  2sqlem3  14324