Theorem ee30 16613

Description: e30 16612 without virtual deductions.

Hypotheses

Ref	Expression
ee30.1	|- (ph -> (ps -> (ch -> th)))
ee30.2	|- ta
ee30.3	|- (th -> (ta -> et))

Assertion

Ref	Expression
ee30	|- (ph -> (ps -> (ch -> et)))

Proof of Theorem ee30

Step	Hyp	Ref	Expression
1		ee30.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		ee30.2	. . . . 5 |- ta
3	2	a1i 8	. . . 4 |- (ch -> ta)
4	3	a1i 8	. . 3 |- (ps -> (ch -> ta))
5	4	a1i 8	. 2 |- (ph -> (ps -> (ch -> ta)))
6		ee30.3	. 2 |- (th -> (ta -> et))
7	1, 5, 6	ee33 5844	1 |- (ph -> (ps -> (ch -> et)))

Syntax hints:   -> wi 3

This theorem is referenced by:  ee30an 16615

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

Copyright terms: Public domain