Theorem simp1bi 961

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
simp1bi	|- ( ph -> ps )

Proof of Theorem simp1bi

Step	Hyp	Ref	Expression
1		3simp1bi.1	. . 3 |- ( ph <-> ( ps /\ ch /\ th ) )
2	1	biimpi 119	. 2 |- ( ph -> ( ps /\ ch /\ th ) )
3	2	simp1d 958	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   <-> wb 104   /\ w3a 927

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

This theorem depends on definitions:  df-bi 116  df-3an 929

This theorem is referenced by:  limord  4246  smores2  6097  smofvon2dm  6099  smofvon  6102  errel  6341  lincmb01cmp  9569  iccf1o  9570  elfznn0  9677  elfzouz  9711  ef01bndlem  11212  sin01bnd  11213  cos01bnd  11214  sin01gt0  11217  cos01gt0  11218  sin02gt0  11219