Theorem ee30an 16615

Description: Conjunction form of ee30 16613.

Hypotheses

Ref	Expression
ee30an.1	|- (ph -> (ps -> (ch -> th)))
ee30an.2	|- ta
ee30an.3	|- ((th /\ ta) -> et)

Assertion

Ref	Expression
ee30an	|- (ph -> (ps -> (ch -> et)))

Proof of Theorem ee30an

Step	Hyp	Ref	Expression
1		ee30an.1	. 2 |- (ph -> (ps -> (ch -> th)))
2		ee30an.2	. 2 |- ta
3		ee30an.3	. . 3 |- ((th /\ ta) -> et)
4	3	ex 402	. 2 |- (th -> (ta -> et))
5	1, 2, 4	ee30 16613	1 |- (ph -> (ps -> (ch -> et)))

Syntax hints:   -> wi 3   /\ wa 240

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