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Metamath Proof Explorer

Theorem e1a

Description: A Virtual deduction elimination rule. syl is e1a without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1a.1	$⊢ (φ \to ψ)$
	e1a.2	$⊢ ψ \to χ$
Assertion	e1a	$⊢ (φ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		e1a.1	$⊢ (φ \to ψ)$
2		e1a.2	$⊢ ψ \to χ$
3	1	in1	$⊢ φ \to ψ$
4	3 2	syl	$⊢ φ \to χ$
5	4	dfvd1ir	$⊢ (φ \to χ)$