Theorem ee02an 38924

Description: e02an 38923 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee02an.1	|- ph
ee02an.2	|- ( ps -> ( ch -> th ) )
ee02an.3	|- ( ( ph /\ th ) -> ta )

Assertion

Ref	Expression
ee02an	|- ( ps -> ( ch -> ta ) )

Proof of Theorem ee02an

Step	Hyp	Ref	Expression
1		ee02an.1	. 2 |- ph
2		ee02an.2	. 2 |- ( ps -> ( ch -> th ) )
3		ee02an.3	. . 3 |- ( ( ph /\ th ) -> ta )
4	3	ex 450	. 2 |- ( ph -> ( th -> ta ) )
5	1, 2, 4	mpsylsyld 69	1 |- ( ps -> ( ch -> ta ) )

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)