Theorem orbi1d

Description: Deduction adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	bid.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	orbi1d	$$⊢\phi \to \left(\left(\psi \vee \theta \right)\leftrightarrow \left(\chi \vee \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		bid.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	orbi2d	$$⊢\phi \to \left(\left(\theta \vee \psi \right)\leftrightarrow \left(\theta \vee \chi \right)\right)$$
3		orcom	$$⊢\left(\psi \vee \theta \right)\leftrightarrow \left(\theta \vee \psi \right)$$
4		orcom	$$⊢\left(\chi \vee \theta \right)\leftrightarrow \left(\theta \vee \chi \right)$$
5	2 3 4	3bitr4g	$$⊢\phi \to \left(\left(\psi \vee \theta \right)\leftrightarrow \left(\chi \vee \theta \right)\right)$$