Theorem ee210 16550

Description: e210 16549 without virtual deductions.

Hypotheses

Ref	Expression
ee210.1	|- (ph -> (ps -> ch))
ee210.2	|- (ph -> th)
ee210.3	|- ta
ee210.4	|- (ch -> (th -> (ta -> et)))

Assertion

Ref	Expression
ee210	|- (ph -> (ps -> et))

Proof of Theorem ee210

Step	Hyp	Ref	Expression
1		ee210.1	. 2 |- (ph -> (ps -> ch))
2		ee210.2	. . 3 |- (ph -> th)
3	2	a1d 15	. 2 |- (ph -> (ps -> th))
4		ee210.3	. . . 4 |- ta
5	4	a1i 8	. . 3 |- (ps -> ta)
6	5	a1i 8	. 2 |- (ph -> (ps -> ta))
7		ee210.4	. 2 |- (ch -> (th -> (ta -> et)))
8	1, 3, 6, 7	ee222 1271	1 |- (ph -> (ps -> 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