Theorem con34b

Description: A biconditional form of contraposition. Theorem *4.1 of WhiteheadRussell p. 116. (Contributed by NM, 11-May-1993)

	Ref	Expression
Assertion	con34b	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( ¬ 𝜓 → ¬ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		con3	⊢ ( ( 𝜑 → 𝜓 ) → ( ¬ 𝜓 → ¬ 𝜑 ) )
2		con4	⊢ ( ( ¬ 𝜓 → ¬ 𝜑 ) → ( 𝜑 → 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( ¬ 𝜓 → ¬ 𝜑 ) )