Theorem ee212

Description: e212 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee212.1	|- ( ph -> ( ps -> ch ) )
	ee212.2	|- ( ph -> th )
	ee212.3	|- ( ph -> ( ps -> ta ) )
	ee212.4	|- ( ch -> ( th -> ( ta -> et ) ) )
Assertion	ee212	|- ( ph -> ( ps -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee212.1	|- ( ph -> ( ps -> ch ) )
2		ee212.2	|- ( ph -> th )
3		ee212.3	|- ( ph -> ( ps -> ta ) )
4		ee212.4	|- ( ch -> ( th -> ( ta -> et ) ) )
5	2	a1d	|- ( ph -> ( ps -> th ) )
6	1 5 3 4	ee222	|- ( ph -> ( ps -> et ) )