Theorem ee323

Description: e323 without virtual deductions. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee323.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee323.2	|- ( ph -> ( ps -> ta ) )
	ee323.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
	ee323.4	|- ( th -> ( ta -> ( et -> ze ) ) )
Assertion	ee323	|- ( ph -> ( ps -> ( ch -> ze ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee323.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee323.2	|- ( ph -> ( ps -> ta ) )
3		ee323.3	|- ( ph -> ( ps -> ( ch -> et ) ) )
4		ee323.4	|- ( th -> ( ta -> ( et -> ze ) ) )
5	2	a1dd	|- ( ph -> ( ps -> ( ch -> ta ) ) )
6	1 5 3 4	ee333	|- ( ph -> ( ps -> ( ch -> ze ) ) )