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	⊢ ( ( ( 𝜑 ∨ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ⊽ 𝜓 ) ∨ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		imor	⊢ ( ( ( 𝜑 ∨ 𝜓 ) → 𝜒 ) ↔ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )
2		df-nor	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ¬ ( 𝜑 ∨ 𝜓 ) )
3	2	orbi1i	⊢ ( ( ( 𝜑 ⊽ 𝜓 ) ∨ 𝜒 ) ↔ ( ¬ ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )
4	1 3	bitr4i	⊢ ( ( ( 𝜑 ∨ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ⊽ 𝜓 ) ∨ 𝜒 ) )