Theorem simplbda 607

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 470	. 2 |- ((ph /\ ps) -> (ch /\ th))
3	2	simprd 449	1 |- ((ph /\ ps) -> th)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by: (None)