Theorem norasslem1

Description: This lemma shows the equivalence of two expressions, used in norass . (Contributed by Wolf Lammen, 18-Dec-2023)

	Ref	Expression
Assertion	norasslem1	$$⊢\left(\left(\phi \vee \psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi ⊽\psi \right)\vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		imor	$$⊢\left(\left(\phi \vee \psi \right)\to \chi \right)\leftrightarrow \left(\neg \left(\phi \vee \psi \right)\vee \chi \right)$$
2		df-nor	$$⊢\left(\phi ⊽\psi \right)\leftrightarrow \neg \left(\phi \vee \psi \right)$$
3	2	orbi1i	$$⊢\left(\left(\phi ⊽\psi \right)\vee \chi \right)\leftrightarrow \left(\neg \left(\phi \vee \psi \right)\vee \chi \right)$$
4	1 3	bitr4i	$$⊢\left(\left(\phi \vee \psi \right)\to \chi \right)\leftrightarrow \left(\left(\phi ⊽\psi \right)\vee \chi \right)$$