Theorem ee03 38968

Description: e03 38967 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee03.1	|- ph
ee03.2	|- ( ps -> ( ch -> ( th -> ta ) ) )
ee03.3	|- ( ph -> ( ta -> et ) )

Assertion

Ref	Expression
ee03	|- ( ps -> ( ch -> ( th -> et ) ) )

Proof of Theorem ee03

Step	Hyp	Ref	Expression
1		ee03.1	. . . . 5 |- ph
2	1	a1i 11	. . . 4 |- ( ps -> ph )
3	2	a1d 25	. . 3 |- ( ps -> ( ch -> ph ) )
4	3	a1dd 50	. 2 |- ( ps -> ( ch -> ( th -> ph ) ) )
5		ee03.2	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
6		ee03.3	. 2 |- ( ph -> ( ta -> et ) )
7	4, 5, 6	ee33 38727	1 |- ( ps -> ( ch -> ( th -> 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:  ee03an  38970  suctrALT2  39072