Theorem ee102 16560

Description: e102 16559 without virtual deductions.

Hypotheses

Ref	Expression
ee102.1	|- (ph -> ps)
ee102.2	|- ch
ee102.3	|- (ph -> (th -> ta))
ee102.4	|- (ps -> (ch -> (ta -> et)))

Assertion

Ref	Expression
ee102	|- (ph -> (th -> et))

Proof of Theorem ee102

Step	Hyp	Ref	Expression
1		ee102.1	. . 3 |- (ph -> ps)
2	1	a1d 15	. 2 |- (ph -> (th -> ps))
3		ee102.2	. . . 4 |- ch
4	3	a1i 8	. . 3 |- (th -> ch)
5	4	a1i 8	. 2 |- (ph -> (th -> ch))
6		ee102.3	. 2 |- (ph -> (th -> ta))
7		ee102.4	. 2 |- (ps -> (ch -> (ta -> et)))
8	2, 5, 6, 7	ee222 1271	1 |- (ph -> (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