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Metamath Proof Explorer

Theorem imim1i

Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. Inference associated with imim1 . Its associated inference is syl . (Contributed by NM, 28-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

		Ref	Expression
	Hypothesis	imim1i.1	$⊢ φ \to ψ$
	Assertion	imim1i	$⊢ (ψ \to χ) \to (φ \to χ)$

Proof

Step	Hyp	Ref	Expression
1		imim1i.1	$⊢ φ \to ψ$
2		id	$⊢ χ \to χ$
3	1 2	imim12i	$⊢ (ψ \to χ) \to (φ \to χ)$