Theorem norasslem2 1533

Description: This lemma specializes biimt 360 suitably for the proof of norass 1535. (Contributed by Wolf Lammen, 18-Dec-2023.)

Assertion

Ref	Expression
norasslem2	⊢ (𝜑 → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓)))

Proof of Theorem norasslem2

Step	Hyp	Ref	Expression
1		orc 863	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2		biimt 360	. 2 ⊢ ((𝜑 ∨ 𝜒) → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓)))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜓 ↔ ((𝜑 ∨ 𝜒) → 𝜓)))

Syntax hints:   → wi 4   ↔ wb 205   ∨ wo 843

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

This theorem is referenced by:  norass  1535