Theorem simprbda 381

Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007.)

Hypothesis

Ref	Expression
pm3.26bda.1	|- ( ph -> ( ps <-> ( ch /\ th ) ) )

Assertion

Ref	Expression
simprbda	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem simprbda

Step	Hyp	Ref	Expression
1		pm3.26bda.1	. . 3 |- ( ph -> ( ps <-> ( ch /\ th ) ) )
2	1	biimpa 294	. 2 |- ( ( ph /\ ps ) -> ( ch /\ th ) )
3	2	simpld 111	1 |- ( ( ph /\ ps ) -> ch )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104

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

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  elrabi  2883  cvgratz  11495  tg1  12853  cldss  12899  cnf2  12999  cncnp  13024  blgt0  13196  xblss2ps  13198  xblss2  13199  dvcnp2cntop  13457