Theorem ee01an 38918

Description: e01an 38917 without virtual deductions. sylancr 695 is also a form of e01an 38917 without virtual deduction, 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
ee01an.1	|- ph
ee01an.2	|- ( ps -> ch )
ee01an.3	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
ee01an	|- ( ps -> th )

Proof of Theorem ee01an

Step	Hyp	Ref	Expression
1		ee01an.1	. 2 |- ph
2		ee01an.2	. 2 |- ( ps -> ch )
3		ee01an.3	. 2 |- ( ( ph /\ ch ) -> th )
4	1, 2, 3	sylancr 695	1 |- ( ps -> 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)