Theorem ecase 752

Description: Inference for elimination by cases.

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 373	. 2 |- (ph -> (ps -> ch))
3		ecase.1	. 2 |- (-. ph -> ch)
4		ecase.2	. 2 |- (-. ps -> ch)
5	2, 3, 4	pm2.61nii 131	1 |- ch

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain