Theorem ee102

Description: e102 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee102.1	|- ( ph -> ps )
	ee102.2	|- ch
	ee102.3	|- ( ph -> ( th -> ta ) )
	ee102.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
Assertion	ee102	|- ( ph -> ( th -> et ) )

Proof

Step	Hyp	Ref	Expression
1		ee102.1	|- ( ph -> ps )
2		ee102.2	|- ch
3		ee102.3	|- ( ph -> ( th -> ta ) )
4		ee102.4	|- ( ps -> ( ch -> ( ta -> et ) ) )
5	1	a1d	|- ( ph -> ( th -> ps ) )
6	2	a1i	|- ( th -> ch )
7	6	a1i	|- ( ph -> ( th -> ch ) )
8	5 7 3 4	ee222	|- ( ph -> ( th -> et ) )