Theorem e101 38903

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

Hypotheses

Ref	Expression
e101.1	|- (. ph ->. ps ).
e101.2	|- ch
e101.3	|- (. ph ->. th ).
e101.4	|- ( ps -> ( ch -> ( th -> ta ) ) )

Assertion

Ref	Expression
e101	|- (. ph ->. ta ).

Proof of Theorem e101

Step	Hyp	Ref	Expression
1		e101.1	. 2 |- (. ph ->. ps ).
2		e101.2	. . 3 |- ch
3	2	vd01 38822	. 2 |- (. ph ->. ch ).
4		e101.3	. 2 |- (. ph ->. th ).
5		e101.4	. 2 |- ( ps -> ( ch -> ( th -> ta ) ) )
6	1, 3, 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: (None)