Theorem orbi2iALT 35523

Description: Alternate proof of orbi2i 910. (Contributed by Hongxiu Chen, 29-Jun-2025.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
orbi2iALT.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
orbi2iALT	⊢ ((𝜒 ∨ 𝜑) ↔ (𝜒 ∨ 𝜓))

Proof of Theorem orbi2iALT

Step	Hyp	Ref	Expression
1		orbi2iALT.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	a1i 11	. . 3 ⊢ (¬ 𝜒 → (𝜑 ↔ 𝜓))
3	2	pm5.74i 270	. 2 ⊢ ((¬ 𝜒 → 𝜑) ↔ (¬ 𝜒 → 𝜓))
4		df-or 846	. 2 ⊢ ((𝜒 ∨ 𝜑) ↔ (¬ 𝜒 → 𝜑))
5		df-or 846	. 2 ⊢ ((𝜒 ∨ 𝜓) ↔ (¬ 𝜒 → 𝜓))
6	3, 4, 5	3bitr4i 302	1 ⊢ ((𝜒 ∨ 𝜑) ↔ (𝜒 ∨ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∨ wo 845

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 846

This theorem is referenced by: (None)