Theorem e30an 38973

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e30an.1	|- (. ph ,. ps ,. ch ->. th ).
e30an.2	|- ta
e30an.3	|- ( ( th /\ ta ) -> et )

Assertion

Ref	Expression
e30an	|- (. ph ,. ps ,. ch ->. et ).

Proof of Theorem e30an

Step	Hyp	Ref	Expression
1		e30an.1	. 2 |- (. ph ,. ps ,. ch ->. th ).
2		e30an.2	. 2 |- ta
3		e30an.3	. . 3 |- ( ( th /\ ta ) -> et )
4	3	ex 450	. 2 |- ( th -> ( ta -> et ) )
5	1, 2, 4	e30 38971	1 |- (. ph ,. ps ,. ch ->. et ).

Syntax hints:   -> wi 4   /\ wa 384   (.wvd3 38803

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-3an 1039  df-vd3 38806

This theorem is referenced by: (None)