Theorem e21

Description: A virtual deduction elimination rule (see syl6ci ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e21.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e21.2	$$⊢\left(\phi \to \theta \right)$$
	e21.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
Assertion	e21	$$⊢\left(\phi ,\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e21.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e21.2	$$⊢\left(\phi \to \theta \right)$$
3		e21.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
4	2	vd12	$$⊢\left(\phi ,\psi \to \theta \right)$$
5	1 4 3	e22	$$⊢\left(\phi ,\psi \to \tau \right)$$