Theorem ee012 16558

Description: e012 16557 without virtual deductions.

Hypotheses

Ref	Expression
ee012.1	|- ph
ee012.2	|- (ps -> ch)
ee012.3	|- (ps -> (th -> ta))
ee012.4	|- (ph -> (ch -> (ta -> et)))

Assertion

Ref	Expression
ee012	|- (ps -> (th -> et))

Proof of Theorem ee012

Step	Hyp	Ref	Expression
1		ee012.1	. . . 4 |- ph
2	1	a1i 8	. . 3 |- (th -> ph)
3	2	a1i 8	. 2 |- (ps -> (th -> ph))
4		ee012.2	. . 3 |- (ps -> ch)
5	4	a1d 15	. 2 |- (ps -> (th -> ch))
6		ee012.3	. 2 |- (ps -> (th -> ta))
7		ee012.4	. 2 |- (ph -> (ch -> (ta -> et)))
8	3, 5, 6, 7	ee222 1271	1 |- (ps -> (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