Theorem ee30an

Description: Conjunction form of ee30 . (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee30an.2	|- ta
	ee30an.3	|- ( ( th /\ ta ) -> et )
Assertion	ee30an	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee30an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee30an.2	|- ta
3		ee30an.3	|- ( ( th /\ ta ) -> et )
4	3	ex	|- ( th -> ( ta -> et ) )
5	1 2 4	ee30	|- ( ph -> ( ps -> ( ch -> et ) ) )