Theorem con4bid

Description: A contraposition deduction. (Contributed by NM, 21-May-1994)

	Ref	Expression
Hypothesis	con4bid.1	⊢ ( 𝜑 → ( ¬ 𝜓 ↔ ¬ 𝜒 ) )
Assertion	con4bid	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		con4bid.1	⊢ ( 𝜑 → ( ¬ 𝜓 ↔ ¬ 𝜒 ) )
2	1	biimprd	⊢ ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) )
3	2	con4d	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	1	biimpd	⊢ ( 𝜑 → ( ¬ 𝜓 → ¬ 𝜒 ) )
5	3 4	impcon4bid	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )