Theorem mpjaodan 761

Description: Eliminate a disjunction in a deduction. A translation of natural deduction rule \/ E (\/ elimination), see natded in set.mm. (Contributed by Mario Carneiro, 29-May-2016.)

Hypotheses

Ref	Expression
jaodan.1	|- ((ph /\ ps) -> ch)
jaodan.2	|- ((ph /\ th) -> ch)
jaodan.3	|- (ph -> (ps \/ th))

Assertion

Ref	Expression
mpjaodan	|- (ph -> ch)

Proof of Theorem mpjaodan

Step	Hyp	Ref	Expression
1		jaodan.3	. 2 |- (ph -> (ps \/ th))
2		jaodan.1	. . 3 |- ((ph /\ ps) -> ch)
3		jaodan.2	. . 3 |- ((ph /\ th) -> ch)
4	2, 3	jaodan 760	. 2 |- ((ph /\ (ps \/ th)) -> ch)
5	1, 4	mpdan 649	1 |- (ph -> ch)

Syntax hints:   -> wi 4   \/ wo 357   /\ 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-or 359  df-an 360

This theorem is referenced by: (None)