Theorem xchbinxr

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

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

Proof

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