Theorem ccase 912

Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.) (Proof shortened by Wolf Lammen, 6-Jan-2013.)

Hypotheses

Ref	Expression
ccase.1	|- ((ph /\ ps) -> ta)
ccase.2	|- ((ch /\ ps) -> ta)
ccase.3	|- ((ph /\ th) -> ta)
ccase.4	|- ((ch /\ th) -> ta)

Assertion

Ref	Expression
ccase	|- (((ph \/ ch) /\ (ps \/ th)) -> ta)

Proof of Theorem ccase

Step	Hyp	Ref	Expression
1		ccase.1	. . 3 |- ((ph /\ ps) -> ta)
2		ccase.2	. . 3 |- ((ch /\ ps) -> ta)
3	1, 2	jaoian 759	. 2 |- (((ph \/ ch) /\ ps) -> ta)
4		ccase.3	. . 3 |- ((ph /\ th) -> ta)
5		ccase.4	. . 3 |- ((ch /\ th) -> ta)
6	4, 5	jaoian 759	. 2 |- (((ph \/ ch) /\ th) -> ta)
7	3, 6	jaodan 760	1 |- (((ph \/ ch) /\ (ps \/ th)) -> ta)

Syntax hints:   -> wi 4   \/ wo 357   /\ 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:  ccased  913  ccase2  914  undif3  3516