Theorem ee31

Description: e31 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee31.2	|- ( ph -> ta )
	ee31.3	|- ( th -> ( ta -> et ) )
Assertion	ee31	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee31.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee31.2	|- ( ph -> ta )
3		ee31.3	|- ( th -> ( ta -> et ) )
4	2	a1d	|- ( ph -> ( ch -> ta ) )
5	4	a1d	|- ( ph -> ( ps -> ( ch -> ta ) ) )
6	1 5 3	ee33	|- ( ph -> ( ps -> ( ch -> et ) ) )