Theorem impor

Description: An equivalent formula for implying a disjunction. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Assertion	impor	$$⊢\left(\phi \to \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\left(\neg \phi \vee \psi \right)\vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imor	$$⊢\left(\phi \to \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\neg \phi \vee \left(\psi \vee \chi \right)\right)$$
2		orass	$$⊢\left(\left(\neg \phi \vee \psi \right)\vee \chi \right)\leftrightarrow \left(\neg \phi \vee \left(\psi \vee \chi \right)\right)$$
3	1 2	bitr4i	$$⊢\left(\phi \to \left(\psi \vee \chi \right)\right)\leftrightarrow \left(\left(\neg \phi \vee \psi \right)\vee \chi \right)$$