Theorem e12an 38952

Description: Conjunction form of e12 38951 (see syl6an 568). (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e12an.1	|- (. ph ->. ps ).
e12an.2	|- (. ph ,. ch ->. th ).
e12an.3	|- ( ( ps /\ th ) -> ta )

Assertion

Ref	Expression
e12an	|- (. ph ,. ch ->. ta ).

Proof of Theorem e12an

Step	Hyp	Ref	Expression
1		e12an.1	. 2 |- (. ph ->. ps ).
2		e12an.2	. 2 |- (. ph ,. ch ->. th ).
3		e12an.3	. . 3 |- ( ( ps /\ th ) -> ta )
4	3	ex 450	. 2 |- ( ps -> ( th -> ta ) )
5	1, 2, 4	e12 38951	1 |- (. ph ,. ch ->. ta ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd1 38785   (.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-vd1 38786  df-vd2 38794

This theorem is referenced by:  sstrALT2VD  39069