Theorem simplbda 384

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

Hypothesis

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

Assertion

Ref	Expression
simplbda	|- ( ( ph /\ ps ) -> th )

Proof of Theorem simplbda

Step	Hyp	Ref	Expression
1		pm3.26bda.1	. . 3 |- ( ph -> ( ps <-> ( ch /\ th ) ) )
2	1	biimpa 296	. 2 |- ( ( ph /\ ps ) -> ( ch /\ th ) )
3	2	simprd 114	1 |- ( ( ph /\ ps ) -> th )

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:  suppcofn  6444  rhmpropd  14332  lsslmod  14459  tgcl  14858  cldopn  14901  cncnp  15024  blgt0  15196  xblss2ps  15198  xblss2  15199  mopni  15276  metrest  15300  dvcl  15477  dvcnp2cntop  15493