Theorem ecase 983

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 450	. 2 |- ( ph -> ( ps -> ch ) )
3		ecase.1	. 2 |- ( -. ph -> ch )
4		ecase.2	. 2 |- ( -. ps -> ch )
5	2, 3, 4	pm2.61nii 178	1 |- ch

Syntax hints:   -. wn 3   -> wi 4   /\ 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-an 386

This theorem is referenced by:  hashprb  13185  txindislem  21436  1to3vfriswmgr  27144