Theorem xchnxbir

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

	Ref	Expression
Hypotheses	xchnxbir.1	$$⊢\neg \phi \leftrightarrow \psi$$
	xchnxbir.2	$$⊢\chi \leftrightarrow \phi$$
Assertion	xchnxbir	$$⊢\neg \chi \leftrightarrow \psi$$

Proof

Step	Hyp	Ref	Expression
1		xchnxbir.1	$$⊢\neg \phi \leftrightarrow \psi$$
2		xchnxbir.2	$$⊢\chi \leftrightarrow \phi$$
3	2	bicomi	$$⊢\phi \leftrightarrow \chi$$
4	1 3	xchnxbi	$$⊢\neg \chi \leftrightarrow \psi$$