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	$$⊢\phi \leftrightarrow \psi$$
Assertion	orbi2iALT	$$⊢\left(\chi \vee \phi \right)\leftrightarrow \left(\chi \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orbi2iALT.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢\neg \chi \to \left(\phi \leftrightarrow \psi \right)$$
3	2	pm5.74i	$$⊢\left(\neg \chi \to \phi \right)\leftrightarrow \left(\neg \chi \to \psi \right)$$
4		df-or	$$⊢\left(\chi \vee \phi \right)\leftrightarrow \left(\neg \chi \to \phi \right)$$
5		df-or	$$⊢\left(\chi \vee \psi \right)\leftrightarrow \left(\neg \chi \to \psi \right)$$
6	3 4 5	3bitr4i	$$⊢\left(\chi \vee \phi \right)\leftrightarrow \left(\chi \vee \psi \right)$$