Theorem con1bii

Description: A contraposition inference. (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 13-Oct-2012)

	Ref	Expression
Hypothesis	con1bii.1	$$⊢\neg \phi \leftrightarrow \psi$$
Assertion	con1bii	$$⊢\neg \psi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		con1bii.1	$$⊢\neg \phi \leftrightarrow \psi$$
2		notnotb	$$⊢\phi \leftrightarrow \neg \neg \phi$$
3	2 1	xchbinx	$$⊢\phi \leftrightarrow \neg \psi$$
4	3	bicomi	$$⊢\neg \psi \leftrightarrow \phi$$