Theorem con2b

Description: Contraposition. Bidirectional version of con2 . (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	con2b	⊢ ( ( 𝜑 → ¬ 𝜓 ) ↔ ( 𝜓 → ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		con2	⊢ ( ( 𝜑 → ¬ 𝜓 ) → ( 𝜓 → ¬ 𝜑 ) )
2		con2	⊢ ( ( 𝜓 → ¬ 𝜑 ) → ( 𝜑 → ¬ 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 → ¬ 𝜓 ) ↔ ( 𝜓 → ¬ 𝜑 ) )