Theorem ecased 985

Description: Deduction for elimination by cases. (Contributed by NM, 8-Oct-2012.)

Hypotheses

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

Assertion

Ref	Expression
ecased	|- ( ph -> th )

Proof of Theorem ecased

Step	Hyp	Ref	Expression
1		ecased.1	. 2 |- ( ph -> ( -. ps -> th ) )
2		ecased.2	. 2 |- ( ph -> ( -. ch -> th ) )
3		pm3.11 520	. . 3 |- ( -. ( -. ps \/ -. ch ) -> ( ps /\ ch ) )
4		ecased.3	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
5	3, 4	syl5 34	. 2 |- ( ph -> ( -. ( -. ps \/ -. ch ) -> th ) )
6	1, 2, 5	ecase3d 984	1 |- ( ph -> th )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by:  ecase3ad  986  itgsplitioo  23604  rolle  23753  dalaw  35172