Theorem e202

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e202.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e202.2	$$⊢\theta$$
	e202.3	$$⊢\left(\phi ,\psi \to \tau \right)$$
	e202.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
Assertion	e202	$$⊢\left(\phi ,\psi \to \eta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e202.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e202.2	$$⊢\theta$$
3		e202.3	$$⊢\left(\phi ,\psi \to \tau \right)$$
4		e202.4	$$⊢\chi \to \left(\theta \to \left(\tau \to \eta \right)\right)$$
5	2	vd02	$$⊢\left(\phi ,\psi \to \theta \right)$$
6	1 5 3 4	e222	$$⊢\left(\phi ,\psi \to \eta \right)$$