Theorem ee221

Description: e221 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee221.1	|- ( ph -> ( ps -> ch ) )
	ee221.2	|- ( ph -> ( ps -> th ) )
	ee221.3	|- ( ph -> ta )
	ee221.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	ee221	|- ( ph -> ( ps -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee221.1	|- ( ph -> ( ps -> ch ) )
2		ee221.2	|- ( ph -> ( ps -> th ) )
3		ee221.3	|- ( ph -> ta )
4		ee221.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	3	a1d	|- ( ph -> ( ps -> ta ) )
6	1 2 5 4	ee222	|- ( ph -> ( ps -> et ) )