Theorem ee03an 38970

Description: Conjunction form of ee03 38968. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee03an.1	|- ph
ee03an.2	|- ( ps -> ( ch -> ( th -> ta ) ) )
ee03an.3	|- ( ( ph /\ ta ) -> et )

Assertion

Ref	Expression
ee03an	|- ( ps -> ( ch -> ( th -> et ) ) )

Proof of Theorem ee03an

Step	Hyp	Ref	Expression
1		ee03an.1	. 2 |- ph
2		ee03an.2	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
3		ee03an.3	. . 3 |- ( ( ph /\ ta ) -> et )
4	3	ex 450	. 2 |- ( ph -> ( ta -> et ) )
5	1, 2, 4	ee03 38968	1 |- ( ps -> ( ch -> ( th -> et ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)