Theorem el1

Description: A Virtual deduction elimination rule. syl is el1 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el1.1	$$⊢\left(\phi \to \psi \right)$$
	el1.2	$$⊢\psi \to \chi$$
Assertion	el1	$$⊢\left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		el1.1	$$⊢\left(\phi \to \psi \right)$$
2		el1.2	$$⊢\psi \to \chi$$
3	1	in1	$$⊢\phi \to \psi$$
4	3 2	syl	$$⊢\phi \to \chi$$
5	4	dfvd1ir	$$⊢\left(\phi \to \chi \right)$$