Theorem con1bid

Description: A contraposition deduction. (Contributed by NM, 9-Oct-1999)

	Ref	Expression
Hypothesis	con1bid.1	$$⊢\phi \to \left(\neg \psi \leftrightarrow \chi \right)$$
Assertion	con1bid	$$⊢\phi \to \left(\neg \chi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con1bid.1	$$⊢\phi \to \left(\neg \psi \leftrightarrow \chi \right)$$
2	1	bicomd	$$⊢\phi \to \left(\chi \leftrightarrow \neg \psi \right)$$
3	2	con2bid	$$⊢\phi \to \left(\psi \leftrightarrow \neg \chi \right)$$
4	3	bicomd	$$⊢\phi \to \left(\neg \chi \leftrightarrow \psi \right)$$