Theorem notbii

Description: Negate both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 19-May-2013)

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

Proof

Step	Hyp	Ref	Expression
1		notbii.1	$$⊢\phi \leftrightarrow \psi$$
2		notbi	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\neg \phi \leftrightarrow \neg \psi \right)$$
3	1 2	mpbi	$$⊢\neg \phi \leftrightarrow \neg \psi$$