Theorem orbi2iALT

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

	Ref	Expression
Hypothesis	orbi2iALT.1	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	orbi2iALT	⊢ ( ( 𝜒 ∨ 𝜑 ) ↔ ( 𝜒 ∨ 𝜓 ) )

Proof

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