Theorem ccase

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

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

Proof

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