Theorem con1bid

Description: A contraposition deduction. (Contributed by NM, 9-Oct-1999)

	Ref	Expression
Hypothesis	con1bid.1	⊢ ( 𝜑 → ( ¬ 𝜓 ↔ 𝜒 ) )
Assertion	con1bid	⊢ ( 𝜑 → ( ¬ 𝜒 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		con1bid.1	⊢ ( 𝜑 → ( ¬ 𝜓 ↔ 𝜒 ) )
2	1	bicomd	⊢ ( 𝜑 → ( 𝜒 ↔ ¬ 𝜓 ) )
3	2	con2bid	⊢ ( 𝜑 → ( 𝜓 ↔ ¬ 𝜒 ) )
4	3	bicomd	⊢ ( 𝜑 → ( ¬ 𝜒 ↔ 𝜓 ) )