Theorem 3jaodan

Description: Disjunction of three antecedents (deduction). (Contributed by NM, 14-Oct-2005)

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

Proof

Step	Hyp	Ref	Expression
1		3jaodan.1	|- ( ( ph /\ ps ) -> ch )
2		3jaodan.2	|- ( ( ph /\ th ) -> ch )
3		3jaodan.3	|- ( ( ph /\ ta ) -> ch )
4	1	ex	|- ( ph -> ( ps -> ch ) )
5	2	ex	|- ( ph -> ( th -> ch ) )
6	3	ex	|- ( ph -> ( ta -> ch ) )
7	4 5 6	3jaod	|- ( ph -> ( ( ps \/ th \/ ta ) -> ch ) )
8	7	imp	|- ( ( ph /\ ( ps \/ th \/ ta ) ) -> ch )