Theorem ee13an 38977

Description: e13an 38976 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee13an.1	|- ( ph -> ps )
ee13an.2	|- ( ph -> ( ch -> ( th -> ta ) ) )
ee13an.3	|- ( ( ps /\ ta ) -> et )

Assertion

Ref	Expression
ee13an	|- ( ph -> ( ch -> ( th -> et ) ) )

Proof of Theorem ee13an

Step	Hyp	Ref	Expression
1		ee13an.1	. 2 |- ( ph -> ps )
2		ee13an.2	. 2 |- ( ph -> ( ch -> ( th -> ta ) ) )
3		ee13an.3	. . 3 |- ( ( ps /\ ta ) -> et )
4	3	ex 450	. 2 |- ( ps -> ( ta -> et ) )
5	1, 2, 4	ee13 38710	1 |- ( ph -> ( 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)