Theorem ee333

Description: e333 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee333.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee333.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
	ee333.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
	ee333.4	|- ( th -> ( ta -> ( et -> ze ) ) )
Assertion	ee333	|- ( ph -> ( ps -> ( ch -> ze ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee333.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee333.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
3		ee333.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
4		ee333.4	|- ( th -> ( ta -> ( et -> ze ) ) )
5	1	3imp	|- ( ( ph /\ ps /\ ch ) -> th )
6	2	3imp	|- ( ( ph /\ ps /\ ch ) -> ta )
7	3	3imp	|- ( ( ph /\ ps /\ ch ) -> et )
8	5 6 7 4	syl3c	|- ( ( ph /\ ps /\ ch ) -> ze )
9	8	3exp	|- ( ph -> ( ps -> ( ch -> ze ) ) )