Theorem vd02 38823

Description: Two virtual hypotheses virtually infer a theorem. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
vd02.1	|- ph

Assertion

Ref	Expression
vd02	|- (. ps ,. ch ->. ph ).

Proof of Theorem vd02

Step	Hyp	Ref	Expression
1		vd02.1	. . . 4 |- ph
2	1	a1i 11	. . 3 |- ( ch -> ph )
3	2	a1i 11	. 2 |- ( ps -> ( ch -> ph ) )
4	3	dfvd2ir 38802	1 |- (. ps ,. ch ->. ph ).

Syntax hints:   -> wi 4   (.wvd2 38793

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-vd2 38794

This theorem is referenced by:  e220  38862  e202  38864  e022  38866  e002  38868  e020  38870  e200  38872  e02  38922  e20  38954