Theorem ee123

Description: e123 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee123.1	|- ( ph -> ps )
	ee123.2	|- ( ph -> ( ch -> th ) )
	ee123.3	|- ( ph -> ( ch -> ( ta -> et ) ) )
	ee123.4	|- ( ps -> ( th -> ( et -> ze ) ) )
Assertion	ee123	|- ( ph -> ( ch -> ( ta -> ze ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee123.1	|- ( ph -> ps )
2		ee123.2	|- ( ph -> ( ch -> th ) )
3		ee123.3	|- ( ph -> ( ch -> ( ta -> et ) ) )
4		ee123.4	|- ( ps -> ( th -> ( et -> ze ) ) )
5	1	a1d	|- ( ph -> ( ta -> ps ) )
6	5	a1d	|- ( ph -> ( ch -> ( ta -> ps ) ) )
7	2	a1dd	|- ( ph -> ( ch -> ( ta -> th ) ) )
8	6 7 3 4	ee333	|- ( ph -> ( ch -> ( ta -> ze ) ) )