Theorem ecase3ad 911

Description: Deduction for elimination by cases. (Contributed by NM, 24-May-2013.)

Hypotheses

Ref	Expression
ecase3ad.1	|- (ph -> (ps -> th))
ecase3ad.2	|- (ph -> (ch -> th))
ecase3ad.3	|- (ph -> ((-. ps /\ -. ch) -> th))

Assertion

Ref	Expression
ecase3ad	|- (ph -> th)

Proof of Theorem ecase3ad

Step	Hyp	Ref	Expression
1		notnot2 104	. . 3 |- (-. -. ps -> ps)
2		ecase3ad.1	. . 3 |- (ph -> (ps -> th))
3	1, 2	syl5 28	. 2 |- (ph -> (-. -. ps -> th))
4		notnot2 104	. . 3 |- (-. -. ch -> ch)
5		ecase3ad.2	. . 3 |- (ph -> (ch -> th))
6	4, 5	syl5 28	. 2 |- (ph -> (-. -. ch -> th))
7		ecase3ad.3	. 2 |- (ph -> ((-. ps /\ -. ch) -> th))
8	3, 6, 7	ecased 910	1 |- (ph -> th)

Syntax hints:  -. wn 3   -> wi 4   /\ 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)