Theorem ccase2 914

Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.)

Hypotheses

Ref	Expression
ccase2.1	|- ((ph /\ ps) -> ta)
ccase2.2	|- (ch -> ta)
ccase2.3	|- (th -> ta)

Assertion

Ref	Expression
ccase2	|- (((ph \/ ch) /\ (ps \/ th)) -> ta)

Proof of Theorem ccase2

Step	Hyp	Ref	Expression
1		ccase2.1	. 2 |- ((ph /\ ps) -> ta)
2		ccase2.2	. . 3 |- (ch -> ta)
3	2	adantr 451	. 2 |- ((ch /\ ps) -> ta)
4		ccase2.3	. . 3 |- (th -> ta)
5	4	adantl 452	. 2 |- ((ph /\ th) -> ta)
6	4	adantl 452	. 2 |- ((ch /\ th) -> ta)
7	1, 3, 5, 6	ccase 912	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: (None)