Theorem ee13

Description: e13 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13.1	|- ( ph -> ps )
	ee13.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
	ee13.3	|- ( ps -> ( ta -> et ) )
Assertion	ee13	|- ( ph -> ( ch -> ( th -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee13.1	|- ( ph -> ps )
2		ee13.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
3		ee13.3	|- ( ps -> ( ta -> et ) )
4	1 3	syl	|- ( ph -> ( ta -> et ) )
5	2 4	syl6d	|- ( ph -> ( ch -> ( th -> et ) ) )