This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ (φ \to ψ)$
	el1.2	$⊢ ψ \to χ$
Assertion	el1	$⊢ (φ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		el1.1	$⊢ (φ \to ψ)$
2		el1.2	$⊢ ψ \to χ$
3	1	in1	$⊢ φ \to ψ$
4	3 2	syl	$⊢ φ \to χ$
5	4	dfvd1ir	$⊢ (φ \to χ)$