Theorem e002 38868

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

Hypotheses

Ref	Expression
e002.1	|- ph
e002.2	|- ps
e002.3	|- (. ch ,. th ->. ta ).
e002.4	|- ( ph -> ( ps -> ( ta -> et ) ) )

Assertion

Ref	Expression
e002	|- (. ch ,. th ->. et ).

Proof of Theorem e002

Step	Hyp	Ref	Expression
1		e002.1	. . 3 |- ph
2	1	vd02 38823	. 2 |- (. ch ,. th ->. ph ).
3		e002.2	. . 3 |- ps
4	3	vd02 38823	. 2 |- (. ch ,. th ->. ps ).
5		e002.3	. 2 |- (. ch ,. th ->. ta ).
6		e002.4	. 2 |- ( ph -> ( ps -> ( ta -> et ) ) )
7	2, 4, 5, 6	e222 38861	1 |- (. ch ,. th ->. et ).

Syntax hints:   -> wi 4   (.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)