Theorem e22

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e22.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e22.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
	e22.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
Assertion	e22	$$⊢\left(\phi ,\psi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e22.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e22.2	$$⊢\left(\phi ,\psi \to \theta \right)$$
3		e22.3	$$⊢\chi \to \left(\theta \to \tau \right)$$
4	3	a1i	$$⊢\chi \to \left(\chi \to \left(\theta \to \tau \right)\right)$$
5	1 1 2 4	e222	$$⊢\left(\phi ,\psi \to \tau \right)$$