Theorem xchbinxr

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

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

Proof

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