Theorem norasslem3 1565

Description: This lemma specializes biorf 949 suitably for the proof of norass 1566. (Contributed by Wolf Lammen, 18-Dec-2023.)

Assertion

Ref	Expression
norasslem3	⊢ (¬ 𝜑 → ((𝜓 → 𝜒) ↔ ((𝜑 ∨ 𝜓) → 𝜒)))

Proof of Theorem norasslem3

Step	Hyp	Ref	Expression
1		biorf 949	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
2	1	imbi1d 344	1 ⊢ (¬ 𝜑 → ((𝜓 → 𝜒) ↔ ((𝜑 ∨ 𝜓) → 𝜒)))

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

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

This theorem is used by:  norass  1566