Theorem e200 38872

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

Hypotheses

Ref	Expression
e200.1	|- (. ph ,. ps ->. ch ).
e200.2	|- th
e200.3	|- ta
e200.4	|- ( ch -> ( th -> ( ta -> et ) ) )

Assertion

Ref	Expression
e200	|- (. ph ,. ps ->. et ).

Proof of Theorem e200

Step	Hyp	Ref	Expression
1		e200.1	. 2 |- (. ph ,. ps ->. ch ).
2		e200.2	. . 3 |- th
3	2	vd02 38823	. 2 |- (. ph ,. ps ->. th ).
4		e200.3	. . 3 |- ta
5	4	vd02 38823	. 2 |- (. ph ,. ps ->. ta ).
6		e200.4	. 2 |- ( ch -> ( th -> ( ta -> et ) ) )
7	1, 3, 5, 6	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: (None)