Theorem simplbda 382

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 294	. 2 |- ( ( ph /\ ps ) -> ( ch /\ th ) )
3	2	simprd 113	1 |- ( ( ph /\ ps ) -> th )

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:  tgcl  12858  cldopn  12901  cncnp  13024  blgt0  13196  xblss2ps  13198  xblss2  13199  mopni  13276  metrest  13300  dvcl  13446  dvcnp2cntop  13457