Theorem norasslem1 1532

Description: This lemma shows the equivalence of two expressions, used in norass 1535. (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 849	. 2 ⊢ (((𝜑 ∨ 𝜓) → 𝜒) ↔ (¬ (𝜑 ∨ 𝜓) ∨ 𝜒))
2		df-nor 1523	. . 3 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
3	2	orbi1i 910	. 2 ⊢ (((𝜑 ⊽ 𝜓) ∨ 𝜒) ↔ (¬ (𝜑 ∨ 𝜓) ∨ 𝜒))
4	1, 3	bitr4i 277	1 ⊢ (((𝜑 ∨ 𝜓) → 𝜒) ↔ ((𝜑 ⊽ 𝜓) ∨ 𝜒))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∨ wo 843   ⊽ wnor 1522

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 844  df-nor 1523

This theorem is referenced by:  norass  1535