Metamath Proof Explorer


Theorem vd03

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.)

Ref Expression
Hypothesis vd03.1
|- ph
Assertion vd03
|- (. ps ,. ch ,. th ->. ph ).

Proof

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