Theorem vd13

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 a two additional hypotheses. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd13.1	$$⊢\left(\phi \to \psi \right)$$
Assertion	vd13	$$⊢\left(\phi ,\chi ,\theta \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		vd13.1	$$⊢\left(\phi \to \psi \right)$$
2	1	in1	$$⊢\phi \to \psi$$
3	2	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$
4	3	a1dd	$$⊢\phi \to \left(\chi \to \left(\theta \to \psi \right)\right)$$
5	4	dfvd3ir	$$⊢\left(\phi ,\chi ,\theta \to \psi \right)$$