Theorem vd23

Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	vd23.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
Assertion	vd23	$$⊢\left(\phi ,\psi ,\theta \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		vd23.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2	1	dfvd2i	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	2	a1dd	$$⊢\phi \to \left(\psi \to \left(\theta \to \chi \right)\right)$$
4	3	dfvd3ir	$$⊢\left(\phi ,\psi ,\theta \to \chi \right)$$