Theorem ee022 16532

Description: e022 16531 without virtual deductions.

Hypotheses

Ref	Expression
ee022.1	|- ph
ee022.2	|- (ps -> (ch -> th))
ee022.3	|- (ps -> (ch -> ta))
ee022.4	|- (ph -> (th -> (ta -> et)))

Assertion

Ref	Expression
ee022	|- (ps -> (ch -> et))

Proof of Theorem ee022

Step	Hyp	Ref	Expression
1		ee022.1	. . . 4 |- ph
2	1	a1i 8	. . 3 |- (ch -> ph)
3	2	a1i 8	. 2 |- (ps -> (ch -> ph))
4		ee022.2	. 2 |- (ps -> (ch -> th))
5		ee022.3	. 2 |- (ps -> (ch -> ta))
6		ee022.4	. 2 |- (ph -> (th -> (ta -> et)))
7	3, 4, 5, 6	ee222 1271	1 |- (ps -> (ch -> 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