Theorem xchnxbi

Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014)

	Ref	Expression
Hypotheses	xchnxbi.1	⊢ ( ¬ 𝜑 ↔ 𝜓 )
	xchnxbi.2	⊢ ( 𝜑 ↔ 𝜒 )
Assertion	xchnxbi	⊢ ( ¬ 𝜒 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		xchnxbi.1	⊢ ( ¬ 𝜑 ↔ 𝜓 )
2		xchnxbi.2	⊢ ( 𝜑 ↔ 𝜒 )
3	2	notbii	⊢ ( ¬ 𝜑 ↔ ¬ 𝜒 )
4	3 1	bitr3i	⊢ ( ¬ 𝜒 ↔ 𝜓 )