Theorem idn3

Description: Virtual deduction identity rule for three virtual hypotheses. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	idn3	$$⊢\left(\phi ,\psi ,\chi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		idd	$$⊢\psi \to \left(\chi \to \chi \right)$$
2	1	a1i	$$⊢\phi \to \left(\psi \to \left(\chi \to \chi \right)\right)$$
3	2	dfvd3ir	$$⊢\left(\phi ,\psi ,\chi \to \chi \right)$$