Theorem ccase2 989

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 481	. 2 |- ( ( ch /\ ps ) -> ta )
4		ccase2.3	. . 3 |- ( th -> ta )
5	4	adantl 482	. 2 |- ( ( ph /\ th ) -> ta )
6	4	adantl 482	. 2 |- ( ( ch /\ th ) -> ta )
7	1, 3, 5, 6	ccase 987	1 |- ( ( ( ph \/ ch ) /\ ( ps \/ th ) ) -> ta )

Syntax hints:   -> wi 4   \/ wo 383   /\ 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-or 385  df-an 386

This theorem is referenced by:  fctop  20808  cctop  20810