Theorem e22an 38897

Description: Conjunction form of e22 38896. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e22an.1	|- (. ph ,. ps ->. ch ).
e22an.2	|- (. ph ,. ps ->. th ).
e22an.3	|- ( ( ch /\ th ) -> ta )

Assertion

Ref	Expression
e22an	|- (. ph ,. ps ->. ta ).

Proof of Theorem e22an

Step	Hyp	Ref	Expression
1		e22an.1	. 2 |- (. ph ,. ps ->. ch ).
2		e22an.2	. 2 |- (. ph ,. ps ->. th ).
3		e22an.3	. . 3 |- ( ( ch /\ th ) -> ta )
4	3	ex 450	. 2 |- ( ch -> ( th -> ta ) )
5	1, 2, 4	e22 38896	1 |- (. ph ,. ps ->. ta ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd2 38793

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-vd2 38794

This theorem is referenced by: (None)