Theorem ee11an 38915

Description: e11an 38914 without virtual deductions. syl22anc 1327 is also e11an 38914 without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee11an.1	|- ( ph -> ps )
ee11an.2	|- ( ph -> ch )
ee11an.3	|- ( ( ps /\ ch ) -> th )

Assertion

Ref	Expression
ee11an	|- ( ph -> th )

Proof of Theorem ee11an

Step	Hyp	Ref	Expression
1		ee11an.1	. 2 |- ( ph -> ps )
2		ee11an.2	. 2 |- ( ph -> ch )
3		ee11an.3	. . 3 |- ( ( ps /\ ch ) -> th )
4	3	ex 450	. 2 |- ( ps -> ( ch -> th ) )
5	1, 2, 4	sylc 65	1 |- ( ph -> th )

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)