Theorem xchbinx

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

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

Proof

Step	Hyp	Ref	Expression
1		xchbinx.1	$$⊢\phi \leftrightarrow \neg \psi$$
2		xchbinx.2	$$⊢\psi \leftrightarrow \chi$$
3	2	notbii	$$⊢\neg \psi \leftrightarrow \neg \chi$$
4	1 3	bitri	$$⊢\phi \leftrightarrow \neg \chi$$