Theorem ee222

Description: e222 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 7-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee222.1	|- ( ph -> ( ps -> ch ) )
	ee222.2	|- ( ph -> ( ps -> th ) )
	ee222.3	|- ( ph -> ( ps -> ta ) )
	ee222.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	ee222	|- ( ph -> ( ps -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee222.1	|- ( ph -> ( ps -> ch ) )
2		ee222.2	|- ( ph -> ( ps -> th ) )
3		ee222.3	|- ( ph -> ( ps -> ta ) )
4		ee222.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	1	imp	|- ( ( ph /\ ps ) -> ch )
6	2	imp	|- ( ( ph /\ ps ) -> th )
7	3	imp	|- ( ( ph /\ ps ) -> ta )
8	5 6 7 4	syl3c	|- ( ( ph /\ ps ) -> et )
9	8	ex	|- ( ph -> ( ps -> et ) )