Theorem ee13an

Description: e13an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13an.1	|- ( ph -> ps )
	ee13an.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
	ee13an.3	|- ( ( ps /\ ta ) -> et )
Assertion	ee13an	|- ( ph -> ( ch -> ( th -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee13an.1	|- ( ph -> ps )
2		ee13an.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
3		ee13an.3	|- ( ( ps /\ ta ) -> et )
4	3	ex	|- ( ps -> ( ta -> et ) )
5	1 2 4	ee13	|- ( ph -> ( ch -> ( th -> et ) ) )