Metamath Proof Explorer

Theorem vd12

Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and an additional hypothesis. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis vd12.1 φ ψ
Assertion vd12 φ , χ ψ


Step Hyp Ref Expression
1 vd12.1 φ ψ
2 1 in1 φ ψ
3 2 a1d φ χ ψ
4 3 dfvd2ir φ , χ ψ