Theorem 3ecase

Description: Inference for elimination by cases. (Contributed by NM, 13-Jul-2005)

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

Proof

Step	Hyp	Ref	Expression
1		3ecase.1	|- ( -. ph -> th )
2		3ecase.2	|- ( -. ps -> th )
3		3ecase.3	|- ( -. ch -> th )
4		3ecase.4	|- ( ( ph /\ ps /\ ch ) -> th )
5	4	3exp	|- ( ph -> ( ps -> ( ch -> th ) ) )
6	1	2a1d	|- ( -. ph -> ( ps -> ( ch -> th ) ) )
7	5 6	pm2.61i	|- ( ps -> ( ch -> th ) )
8	7 2 3	pm2.61nii	|- th