Theorem ee33VD

Description: Non-virtual deduction form of e33 . The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. ee33 is ee33VD without virtual deductions and was automatically derived from ee33VD .

	Ref	Expression
Hypotheses	ee33VD.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	ee33VD.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
	ee33VD.3	|- ( th -> ( ta -> et ) )
Assertion	ee33VD	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee33VD.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee33VD.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
3		ee33VD.3	|- ( th -> ( ta -> et ) )
4	1 3	syl8	|- ( ph -> ( ps -> ( ch -> ( ta -> et ) ) ) )
5	4	com4r	|- ( ta -> ( ph -> ( ps -> ( ch -> et ) ) ) )
6	2 5	syl8	|- ( ph -> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) )
7		pm2.43cbi	|- ( ( ph -> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) ) <-> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) )
8	7	biimpi	|- ( ( ph -> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) ) -> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) )
9	6 8	e0a	|- ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) )
10		pm2.43cbi	|- ( ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) <-> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) )
11	10	biimpi	|- ( ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) )
12	9 11	e0a	|- ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) )
13		pm2.43cbi	|- ( ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) <-> ( ph -> ( ps -> ( ch -> et ) ) ) )
14	13	biimpi	|- ( ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) -> ( ph -> ( ps -> ( ch -> et ) ) ) )
15	12 14	e0a	|- ( ph -> ( ps -> ( ch -> et ) ) )