Theorem xchnxbir

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

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

Proof

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