Theorem e12

Description: A virtual deduction elimination rule (see sylsyld ). (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e12.1	$$⊢\left(\phi \to \psi \right)$$
	e12.2	$$⊢\left(\phi ,\chi \to \theta \right)$$
	e12.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
Assertion	e12	$$⊢\left(\phi ,\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		e12.1	$$⊢\left(\phi \to \psi \right)$$
2		e12.2	$$⊢\left(\phi ,\chi \to \theta \right)$$
3		e12.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
4	1	vd12	$$⊢\left(\phi ,\chi \to \psi \right)$$
5	4 2 3	e22	$$⊢\left(\phi ,\chi \to \tau \right)$$