Theorem ee200

Description: e200 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee200.1	|- ( ph -> ( ps -> ch ) )
	ee200.2	|- th
	ee200.3	|- ta
	ee200.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	ee200	|- ( ph -> ( ps -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee200.1	|- ( ph -> ( ps -> ch ) )
2		ee200.2	|- th
3		ee200.3	|- ta
4		ee200.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	a1i	|- ( ps -> th )
6	5	a1i	|- ( ph -> ( ps -> th ) )
7	3	a1i	|- ( ps -> ta )
8	7	a1i	|- ( ph -> ( ps -> ta ) )
9	1 6 8 4	ee222	|- ( ph -> ( ps -> et ) )