Theorem e323

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e323.1	|- (. ph ,. ps ,. ch ->. th ).
	e323.2	|- (. ph ,. ps ->. ta ).
	e323.3	|- (. ph ,. ps ,. ch ->. et ).
	e323.4	|- ( th -> ( ta -> ( et -> ze ) ) )
Assertion	e323	|- (. ph ,. ps ,. ch ->. ze ).

Proof

Step	Hyp	Ref	Expression
1		e323.1	|- (. ph ,. ps ,. ch ->. th ).
2		e323.2	|- (. ph ,. ps ->. ta ).
3		e323.3	|- (. ph ,. ps ,. ch ->. et ).
4		e323.4	|- ( th -> ( ta -> ( et -> ze ) ) )
5	1	dfvd3i	|- ( ph -> ( ps -> ( ch -> th ) ) )
6	2	dfvd2i	|- ( ph -> ( ps -> ta ) )
7	3	dfvd3i	|- ( ph -> ( ps -> ( ch -> et ) ) )
8	5 6 7 4	ee323	|- ( ph -> ( ps -> ( ch -> ze ) ) )
9	8	dfvd3ir	|- (. ph ,. ps ,. ch ->. ze ).