Theorem ee21an 38959

Description: e21an 38958 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee21an.1	|- ( ph -> ( ps -> ch ) )
ee21an.2	|- ( ph -> th )
ee21an.3	|- ( ( ch /\ th ) -> ta )

Assertion

Ref	Expression
ee21an	|- ( ph -> ( ps -> ta ) )

Proof of Theorem ee21an

Step	Hyp	Ref	Expression
1		ee21an.1	. 2 |- ( ph -> ( ps -> ch ) )
2		ee21an.2	. 2 |- ( ph -> th )
3		ee21an.3	. . 3 |- ( ( ch /\ th ) -> ta )
4	3	ex 450	. 2 |- ( ch -> ( th -> ta ) )
5	1, 2, 4	syl6ci 71	1 |- ( ph -> ( ps -> 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)