Theorem xchbinx

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

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

Proof

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