Theorem ee33an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee33an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee33an.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
	ee33an.3	|- ( ( th /\ ta ) -> et )
Assertion	ee33an	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee33an.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee33an.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
3		ee33an.3	|- ( ( th /\ ta ) -> et )
4	3	ex	|- ( th -> ( ta -> et ) )
5	1 2 4	ee33	|- ( ph -> ( ps -> ( ch -> et ) ) )