Theorem e120

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e120.1	$$⊢\left(\phi \to \psi \right)$$
	e120.2	$$⊢\left(\phi ,\chi \to \theta \right)$$
	e120.3	$$⊢\tau$$
	e120.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e120	$$⊢\left(\phi ,\chi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e120.1	$$⊢\left(\phi \to \psi \right)$$
2		e120.2	$$⊢\left(\phi ,\chi \to \theta \right)$$
3		e120.3	$$⊢\tau$$
4		e120.4	$$⊢\psi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	1	vd12	$$⊢\left(\phi ,\chi \to \psi \right)$$
6	5 2 3 4	e220	$$⊢\left(\phi ,\chi \to \eta \right)$$