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Metamath Proof Explorer

Theorem jcn

Description: Theorem joining the consequents of two premises. Theorem 8 of Margaris p. 60. (Contributed by NM, 5-Aug-1993) (Proof shortened by Josh Purinton, 29-Dec-2000)

		Ref	Expression
	Assertion	jcn	⊢ ( 𝜑 → ( ¬ 𝜓 → ¬ ( 𝜑 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.27	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
2	1	con3d	⊢ ( 𝜑 → ( ¬ 𝜓 → ¬ ( 𝜑 → 𝜓 ) ) )