Theorem con4bii

Description: A contraposition inference. (Contributed by NM, 21-May-1994)

	Ref	Expression
Hypothesis	con4bii.1	$$⊢\neg \phi \leftrightarrow \neg \psi$$
Assertion	con4bii	$$⊢\phi \leftrightarrow \psi$$

Proof

Step	Hyp	Ref	Expression
1		con4bii.1	$$⊢\neg \phi \leftrightarrow \neg \psi$$
2		notbi	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\neg \phi \leftrightarrow \neg \psi \right)$$
3	1 2	mpbir	$$⊢\phi \leftrightarrow \psi$$