Theorem e020

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

	Ref	Expression
Hypotheses	e020.1	|- ph
	e020.2	|- (. ps ,. ch ->. th ).
	e020.3	|- ta
	e020.4	|- ( ph -> ( th -> ( ta -> et ) ) )
Assertion	e020	|- (. ps ,. ch ->. et ).

Proof

Step	Hyp	Ref	Expression
1		e020.1	|- ph
2		e020.2	|- (. ps ,. ch ->. th ).
3		e020.3	|- ta
4		e020.4	|- ( ph -> ( th -> ( ta -> et ) ) )
5	1	vd02	|- (. ps ,. ch ->. ph ).
6	3	vd02	|- (. ps ,. ch ->. ta ).
7	5 2 6 4	e222	|- (. ps ,. ch ->. et ).