Theorem e220 38862

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

Hypotheses

Ref	Expression
e220.1	|- (. ph ,. ps ->. ch ).
e220.2	|- (. ph ,. ps ->. th ).
e220.3	|- ta
e220.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
e220	|- (. ph ,. ps ->. et ).

Proof of Theorem e220

Step	Hyp	Ref	Expression
1		e220.1	. 2 |- (. ph ,. ps ->. ch ).
2		e220.2	. 2 |- (. ph ,. ps ->. th ).
3		e220.3	. . 3 |- ta
4	3	vd02 38823	. 2 |- (. ph ,. ps ->. ta ).
5		e220.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
6	1, 2, 4, 5	e222 38861	1 |- (. ph ,. ps ->. 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:  e120  38888