Theorem e20

Description: A virtual deduction elimination rule (see syl6mpi ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e20.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e20.2	$$⊢\theta$$
	e20.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
Assertion	e20	$$⊢\left(\phi ,\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e20.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e20.2	$$⊢\theta$$
3		e20.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
4	2	vd02	$$⊢\left(\phi ,\psi \to \theta \right)$$
5	1 4 3	e22	$$⊢\left(\phi ,\psi \to \tau \right)$$