Theorem e30 38971

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e30.1	|- (. ph ,. ps ,. ch ->. th ).
e30.2	|- ta
e30.3	|- ( th -> ( ta -> et ) )

Assertion

Ref	Expression
e30	|- (. ph ,. ps ,. ch ->. et ).

Proof of Theorem e30

Step	Hyp	Ref	Expression
1		e30.1	. 2 |- (. ph ,. ps ,. ch ->. th ).
2		e30.2	. . 3 |- ta
3	2	vd03 38824	. 2 |- (. ph ,. ps ,. ch ->. ta ).
4		e30.3	. 2 |- ( th -> ( ta -> et ) )
5	1, 3, 4	e33 38961	1 |- (. ph ,. ps ,. ch ->. et ).

Syntax hints:   -> wi 4   (.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:  e30an  38973