Theorem ee120 16554

Description: Virtual deduction rule e120 16553 without virtual deduction symbols.

Hypotheses

Ref	Expression
ee120.1	|- (ph -> ps)
ee120.2	|- (ph -> (ch -> th))
ee120.3	|- ta
ee120.4	|- (ps -> (th -> (ta -> et)))

Assertion

Ref	Expression
ee120	|- (ph -> (ch -> et))

Proof of Theorem ee120

Step	Hyp	Ref	Expression
1		ee120.1	. . 3 |- (ph -> ps)
2	1	a1d 15	. 2 |- (ph -> (ch -> ps))
3		ee120.2	. 2 |- (ph -> (ch -> th))
4		ee120.3	. . . 4 |- ta
5	4	a1i 8	. . 3 |- (ch -> ta)
6	5	a1i 8	. 2 |- (ph -> (ch -> ta))
7		ee120.4	. 2 |- (ps -> (th -> (ta -> et)))
8	2, 3, 6, 7	ee222 1271	1 |- (ph -> (ch -> et))

Syntax hints:   -> wi 3

This theorem is referenced by:  pwtrr 16649

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