Theorem ee002 16534

Description: e002 16533 without virtual deductions.

Hypotheses

Ref	Expression
ee002.1	|- ph
ee002.2	|- ps
ee002.3	|- (ch -> (th -> ta))
ee002.4	|- (ph -> (ps -> (ta -> et)))

Assertion

Ref	Expression
ee002	|- (ch -> (th -> et))

Proof of Theorem ee002

Step	Hyp	Ref	Expression
1		ee002.1	. . . 4 |- ph
2	1	a1i 8	. . 3 |- (th -> ph)
3	2	a1i 8	. 2 |- (ch -> (th -> ph))
4		ee002.2	. . . 4 |- ps
5	4	a1i 8	. . 3 |- (th -> ps)
6	5	a1i 8	. 2 |- (ch -> (th -> ps))
7		ee002.3	. 2 |- (ch -> (th -> ta))
8		ee002.4	. 2 |- (ph -> (ps -> (ta -> et)))
9	3, 6, 7, 8	ee222 1271	1 |- (ch -> (th -> et))

Syntax hints:   -> wi 3

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  df-an 242

Copyright terms: Public domain