Theorem norasslem3

Description: This lemma specializes biorf suitably for the proof of norass . (Contributed by Wolf Lammen, 18-Dec-2023)

	Ref	Expression
Assertion	norasslem3	$$⊢\neg \phi \to \left(\left(\psi \to \chi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		biorf	$$⊢\neg \phi \to \left(\psi \leftrightarrow \left(\phi \vee \psi \right)\right)$$
2	1	imbi1d	$$⊢\neg \phi \to \left(\left(\psi \to \chi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\to \chi \right)\right)$$