Theorem ecase3 907

Description: Inference for elimination by cases. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)

Hypotheses

Ref	Expression
ecase3.1	|- (ph -> ch)
ecase3.2	|- (ps -> ch)
ecase3.3	|- (-. (ph \/ ps) -> ch)

Assertion

Ref	Expression
ecase3	|- ch

Proof of Theorem ecase3

Step	Hyp	Ref	Expression
1		ecase3.1	. . 3 |- (ph -> ch)
2		ecase3.2	. . 3 |- (ps -> ch)
3	1, 2	jaoi 368	. 2 |- ((ph \/ ps) -> ch)
4		ecase3.3	. 2 |- (-. (ph \/ ps) -> ch)
5	3, 4	pm2.61i 156	1 |- ch

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357

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

This theorem is referenced by:  equvini  1987  eueq3  3011