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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 → 𝜓 )
	Assertion	imim1i	⊢ ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) )

Proof

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