Theorem ee30

Description: e30 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee30.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee30.2	|- ta
	ee30.3	|- ( th -> ( ta -> et ) )
Assertion	ee30	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee30.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee30.2	|- ta
3		ee30.3	|- ( th -> ( ta -> et ) )
4	2	a1i	|- ( ch -> ta )
5	4	a1i	|- ( ps -> ( ch -> ta ) )
6	5	a1i	|- ( ph -> ( ps -> ( ch -> ta ) ) )
7	1 6 3	ee33	|- ( ph -> ( ps -> ( ch -> et ) ) )