Theorem vd03 38824

Description: A theorem is virtually inferred by the 3 virtual hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd03.1	|- ph

Assertion

Ref	Expression
vd03	|- (. ps ,. ch ,. th ->. ph ).

Proof of Theorem vd03

Step	Hyp	Ref	Expression
1		vd03.1	. . . . 5 |- ph
2	1	a1i 11	. . . 4 |- ( th -> ph )
3	2	a1i 11	. . 3 |- ( ch -> ( th -> ph ) )
4	3	a1i 11	. 2 |- ( ps -> ( ch -> ( th -> ph ) ) )
5	4	dfvd3ir 38809	1 |- (. ps ,. ch ,. th ->. ph ).

Syntax hints:   -> wi 4   (.wvd3 38803

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-3an 1039  df-vd3 38806

This theorem is referenced by:  e03  38967  e30  38971