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Metamath Proof Explorer

Theorem pm2.21i

Description: A contradiction implies anything. Inference associated with pm2.21 . Its associated inference is pm2.24ii . (Contributed by NM, 16-Sep-1993)

		Ref	Expression
	Hypothesis	pm2.21i.1	⊢ ¬ 𝜑
	Assertion	pm2.21i	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21i.1	⊢ ¬ 𝜑
2	1	a1i	⊢ ( ¬ 𝜓 → ¬ 𝜑 )
3	2	con4i	⊢ ( 𝜑 → 𝜓 )