Theorem ee10an 38921

Description: e10an 38920 without virtual deductions. sylancl 694 is also e10an 38920 without virtual deductions, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee10an.1	|- ( ph -> ps )
ee10an.2	|- ch
ee10an.3	|- ( ( ps /\ ch ) -> th )

Assertion

Ref	Expression
ee10an	|- ( ph -> th )

Proof of Theorem ee10an

Step	Hyp	Ref	Expression
1		ee10an.1	. 2 |- ( ph -> ps )
2		ee10an.2	. 2 |- ch
3		ee10an.3	. 2 |- ( ( ps /\ ch ) -> th )
4	1, 2, 3	sylancl 694	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)