Theorem norasslem1 1563

Description: This lemma shows the equivalence of two expressions, used in norass 1566. (Contributed by Wolf Lammen, 18-Dec-2023.)

Assertion

Ref	Expression
norasslem1	⊢ (((𝜑 ∨ 𝜓) → 𝜒) ↔ ((𝜑 ⊽ 𝜓) ∨ 𝜒))

Proof of Theorem norasslem1

Step	Hyp	Ref	Expression
1		imor 866	. 2 ⊢ (((𝜑 ∨ 𝜓) → 𝜒) ↔ (¬ (𝜑 ∨ 𝜓) ∨ 𝜒))
2		df-nor 1558	. . 3 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
3	2	orbi1i 926	. 2 ⊢ (((𝜑 ⊽ 𝜓) ∨ 𝜒) ↔ (¬ (𝜑 ∨ 𝜓) ∨ 𝜒))
4	1, 3	bitr4i 281	1 ⊢ (((𝜑 ∨ 𝜓) → 𝜒) ↔ ((𝜑 ⊽ 𝜓) ∨ 𝜒))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 860   ⊽ wnor 1557

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 861  df-nor 1558

This theorem is used by:  norass  1566