Theorem con2bii

Description: A contraposition inference. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypothesis	con2bii.1	⊢ ( 𝜑 ↔ ¬ 𝜓 )
Assertion	con2bii	⊢ ( 𝜓 ↔ ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		con2bii.1	⊢ ( 𝜑 ↔ ¬ 𝜓 )
2		notnotb	⊢ ( 𝜓 ↔ ¬ ¬ 𝜓 )
3	2 1	xchbinxr	⊢ ( 𝜓 ↔ ¬ 𝜑 )