Theorem ecase 908

Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005.)

Hypotheses

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

Assertion

Ref	Expression
ecase	|- ch

Proof of Theorem ecase

Step	Hyp	Ref	Expression
1		ecase.3	. . 3 |- ((ph /\ ps) -> ch)
2	1	ex 423	. 2 |- (ph -> (ps -> ch))
3		ecase.1	. 2 |- (-. ph -> ch)
4		ecase.2	. 2 |- (-. ps -> ch)
5	2, 3, 4	pm2.61nii 158	1 |- ch

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-an 360

This theorem is referenced by: (None)