Theorem e110 38901

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

Hypotheses

Ref	Expression
e110.1	|- (. ph ->. ps ).
e110.2	|- (. ph ->. ch ).
e110.3	|- th
e110.4	|- ( ps -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
e110	|- (. ph ->. ta ).

Proof of Theorem e110

Step	Hyp	Ref	Expression
1		e110.1	. 2 |- (. ph ->. ps ).
2		e110.2	. 2 |- (. ph ->. ch ).
3		e110.3	. . 3 |- th
4	3	vd01 38822	. 2 |- (. ph ->. th ).
5		e110.4	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
6	1, 2, 4, 5	e111 38899	1 |- (. ph ->. ta ).

Syntax hints:   -> wi 4   (.wvd1 38785

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-vd1 38786

This theorem is referenced by:  2uasbanhVD  39147