Theorem con4bii

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

	Ref	Expression
Hypothesis	con4bii.1	⊢ ( ¬ 𝜑 ↔ ¬ 𝜓 )
Assertion	con4bii	⊢ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		con4bii.1	⊢ ( ¬ 𝜑 ↔ ¬ 𝜓 )
2		notbi	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( ¬ 𝜑 ↔ ¬ 𝜓 ) )
3	1 2	mpbir	⊢ ( 𝜑 ↔ 𝜓 )