Theorem norasslem3 1534

Description: This lemma specializes biorf 934 suitably for the proof of norass 1535. (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 934	. 2 ⊢ (¬ 𝜑 → (𝜓 ↔ (𝜑 ∨ 𝜓)))
2	1	imbi1d 342	1 ⊢ (¬ 𝜑 → ((𝜓 → 𝜒) ↔ ((𝜑 ∨ 𝜓) → 𝜒)))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∨ wo 844

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 845

This theorem is referenced by:  norass  1535