Theorem e11an 38914

Description: Conjunction form of e11 38913. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e11an.1	|- (. ph ->. ps ).
e11an.2	|- (. ph ->. ch ).
e11an.3	|- ( ( ps /\ ch ) -> th )

Assertion

Ref	Expression
e11an	|- (. ph ->. th ).

Proof of Theorem e11an

Step	Hyp	Ref	Expression
1		e11an.1	. 2 |- (. ph ->. ps ).
2		e11an.2	. 2 |- (. ph ->. ch ).
3		e11an.3	. . 3 |- ( ( ps /\ ch ) -> th )
4	3	ex 450	. 2 |- ( ps -> ( ch -> th ) )
5	1, 2, 4	e11 38913	1 |- (. ph ->. 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: (None)