Theorem ee03 16609

Description: e03 16608 without virtual deductions.

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 8	. . . 4 |- (ps -> ph)
3	2	a1d 15	. . 3 |- (ps -> (ch -> ph))
4	3	a1dd 53	. 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 5844	1 |- (ps -> (ch -> (th -> et)))

Syntax hints:   -> wi 3

This theorem is referenced by:  ee03an 16611  suctrALT2 16661

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164

Copyright terms: Public domain