Theorem ee03

Description: e03 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee03.1	|- ph
	ee03.2	|- ( ps -> ( ch -> ( th -> ta ) ) )
	ee03.3	|- ( ph -> ( ta -> et ) )
Assertion	ee03	|- ( ps -> ( ch -> ( th -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee03.1	|- ph
2		ee03.2	|- ( ps -> ( ch -> ( th -> ta ) ) )
3		ee03.3	|- ( ph -> ( ta -> et ) )
4	1	a1i	|- ( ps -> ph )
5	4	a1d	|- ( ps -> ( ch -> ph ) )
6	5	a1dd	|- ( ps -> ( ch -> ( th -> ph ) ) )
7	6 2 3	ee33	|- ( ps -> ( ch -> ( th -> et ) ) )