Theorem simprbda 383

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 296	. 2 |- ( ( ph /\ ps ) -> ( ch /\ th ) )
3	2	simpld 112	1 |- ( ( ph /\ ps ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   <-> wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117

This theorem is used by:  elrabi  2979  cvgratz  12315  subrguss  14593  rhmpropd  14611  lmodfopnelem1  14710  psrbaglecl  15109  tg1  15209  cldss  15255  cnf2  15355  cncnp  15380  blgt0  15552  xblss2ps  15554  xblss2  15555  dvcnp2cntop  15849