Theorem e01an 38917

Description: Conjunction form of e01 38916. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e01an.1	|- ph
e01an.2	|- (. ps ->. ch ).
e01an.3	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
e01an	|- (. ps ->. th ).

Proof of Theorem e01an

Step	Hyp	Ref	Expression
1		e01an.1	. 2 |- ph
2		e01an.2	. 2 |- (. ps ->. ch ).
3		e01an.3	. . 3 |- ( ( ph /\ ch ) -> th )
4	3	ex 450	. 2 |- ( ph -> ( ch -> th ) )
5	1, 2, 4	e01 38916	1 |- (. ps ->. th ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd1 38785

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  df-vd1 38786

This theorem is referenced by:  unipwrVD  39067