Theorem rabbii

Description: Equivalent wff's correspond to equal restricted class abstractions. Inference form of rabbidv . (Contributed by Peter Mazsa, 1-Nov-2019)

	Ref	Expression
Hypothesis	rabbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	rabbii	$$⊢\left\{x\in A|\phi \right\}=\left\{x\in A|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		rabbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \leftrightarrow \psi \right)$$
3	2	rabbiia	$$⊢\left\{x\in A|\phi \right\}=\left\{x\in A|\psi \right\}$$