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 )

Syntax hints:   -> wi 4   /\ wa 104   <-> wb 105

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

This theorem is referenced by:  elrabi  2917  cvgratz  11716  subrguss  13870  rhmpropd  13888  lmodfopnelem1  13958  tg1  14403  cldss  14449  cnf2  14549  cncnp  14574  blgt0  14746  xblss2ps  14748  xblss2  14749  dvcnp2cntop  15043