Theorem simp2bi 960

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 119	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp2d 957	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 925

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-3an 927

This theorem is referenced by:  0ellim  4234  smodm  6070  erdm  6316  ixpfn  6475  dif1en  6649  eluzelz  9089  elfz3nn0  9590  ef01bndlem  11108  sin01bnd  11109  cos01bnd  11110  sin01gt0  11113