Theorem ee202 16530

Description: e202 16529 without virtual deductions.

Hypotheses

Ref	Expression
ee202.1	|- (ph -> (ps -> ch))
ee202.2	|- th
ee202.3	|- (ph -> (ps -> ta))
ee202.4	|- (ch -> (th -> (ta -> et)))

Assertion

Ref	Expression
ee202	|- (ph -> (ps -> et))

Proof of Theorem ee202

Step	Hyp	Ref	Expression
1		ee202.1	. 2 |- (ph -> (ps -> ch))
2		ee202.2	. . . 4 |- th
3	2	a1i 8	. . 3 |- (ps -> th)
4	3	a1i 8	. 2 |- (ph -> (ps -> th))
5		ee202.3	. 2 |- (ph -> (ps -> ta))
6		ee202.4	. 2 |- (ch -> (th -> (ta -> et)))
7	1, 4, 5, 6	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