Theorem ifpnotnotb

Description: Factor conditional logic operator over negation in terms 2 and 3. (Contributed by RP, 21-Apr-2020)

	Ref	Expression
Assertion	ifpnotnotb	$$⊢if-\left(\phi ,\neg \psi ,\neg \chi \right)\leftrightarrow \neg if-\left(\phi ,\psi ,\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ifpnot23	$$⊢\neg if-\left(\phi ,\psi ,\chi \right)\leftrightarrow if-\left(\phi ,\neg \psi ,\neg \chi \right)$$
2	1	bicomi	$$⊢if-\left(\phi ,\neg \psi ,\neg \chi \right)\leftrightarrow \neg if-\left(\phi ,\psi ,\chi \right)$$