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 )

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:  suppcofn  6510  funisfsuppdc  7298  cntzi  14161  rhmpropd  14670  lsslmod  14825  tgcl  15307  cldopn  15350  cncnp  15473  blgt0  15645  xblss2ps  15647  xblss2  15648  mopni  15725  metrest  15749  dvcl  15926  dvcnp2cntop  15942