Theorem e2

Description: A virtual deduction elimination rule. syl6 is e2 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
	e2.2	$$⊢\chi \to \theta$$
Assertion	e2	$$⊢\left(\phi ,\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		e2.1	$$⊢\left(\phi ,\psi \to \chi \right)$$
2		e2.2	$$⊢\chi \to \theta$$
3	1	dfvd2i	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3 2	syl6	$$⊢\phi \to \left(\psi \to \theta \right)$$
5	4	dfvd2ir	$$⊢\left(\phi ,\psi \to \theta \right)$$