Theorem ee33 38727

Description: Non-virtual deduction form of e33 38961. (Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.) 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. The completed Virtual Deduction Proof (not shown) was minimized. The minimized proof is shown.

h1::	|- ( ph -> ( ps -> ( ch -> th ) ) )
h2::	|- ( ph -> ( ps -> ( ch -> ta ) ) )
h3::	|- ( th -> ( ta -> et ) )
4:1,3:	|- ( ph -> ( ps -> ( ch -> ( ta -> et ) ) ) )
5:4:	|- ( ta -> ( ph -> ( ps -> ( ch -> et ) ) ) )
6:2,5:	|- ( ph -> ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) ) )
7:6:	|- ( ps -> ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) ) )
8:7:	|- ( ch -> ( ph -> ( ps -> ( ch -> et ) ) ) )
qed:8:	|- ( ph -> ( ps -> ( ch -> et ) ) )

Hypotheses

Ref	Expression
ee33.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
ee33.2	|- ( ph -> ( ps -> ( ch -> ta ) ) )
ee33.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
ee33	|- ( ph -> ( ps -> ( ch -> et ) ) )

Proof of Theorem ee33

Step	Hyp	Ref	Expression
1		ee33.1	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
2		ee33.2	. 2 |- ( ph -> ( ps -> ( ch -> ta ) ) )
3		ee33.3	. . 3 |- ( th -> ( ta -> et ) )
4	3	imim3i 64	. 2 |- ( ( ch -> th ) -> ( ( ch -> ta ) -> ( ch -> et ) ) )
5	1, 2, 4	syl6c 70	1 |- ( ph -> ( ps -> ( ch -> et ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  truniALT  38751  onfrALTlem2  38761  ee33an  38963  ee03  38968  ee30  38972  ee31  38979  ee32  38986  trintALT  39117