Theorem con2bid

Description: A contraposition deduction. (Contributed by NM, 15-Apr-1995)

	Ref	Expression
Hypothesis	con2bid.1	⊢ ( 𝜑 → ( 𝜓 ↔ ¬ 𝜒 ) )
Assertion	con2bid	⊢ ( 𝜑 → ( 𝜒 ↔ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		con2bid.1	⊢ ( 𝜑 → ( 𝜓 ↔ ¬ 𝜒 ) )
2		con2bi	⊢ ( ( 𝜒 ↔ ¬ 𝜓 ) ↔ ( 𝜓 ↔ ¬ 𝜒 ) )
3	1 2	sylibr	⊢ ( 𝜑 → ( 𝜒 ↔ ¬ 𝜓 ) )