Theorem rabbidv

Description: Equivalent wff's yield equal restricted class abstractions (deduction form). (Contributed by NM, 10-Feb-1995)

	Ref	Expression
Hypothesis	rabbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	rabbidv	$$⊢\phi \to \left\{x\in A|\psi \right\}=\left\{x\in A|\chi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		rabbidv.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2	1	adantr	$$⊢\left(\phi \wedge x\in A\right)\to \left(\psi \leftrightarrow \chi \right)$$
3	2	rabbidva	$$⊢\phi \to \left\{x\in A|\psi \right\}=\left\{x\in A|\chi \right\}$$