Theorem opabbidv

Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction form). (Contributed by NM, 15-May-1995)

	Ref	Expression
Hypothesis	opabbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	opabbidv	$$⊢\phi \to \left\{⟨x,y⟩|\psi \right\}=\left\{⟨x,y⟩|\chi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		opabbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		nfv	$$⊢Ⅎx\phi$$
3		nfv	$$⊢Ⅎy\phi$$
4	2 3 1	opabbid	$$⊢\phi \to \left\{⟨x,y⟩|\psi \right\}=\left\{⟨x,y⟩|\chi \right\}$$