Theorem cbvraldvaOLD

Description: Obsolete version of cbvraldva as of 9-Mar-2025. (Contributed by David Moews, 1-May-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvrexdva.1	$$⊢\left(\phi \wedge x=y\right)\to \left(\psi \leftrightarrow \chi \right)$$
Assertion	cbvraldvaOLD	$$⊢\phi \to \left(\forall x\in A\psi \leftrightarrow \forall y\in A\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		cbvrexdva.1	$$⊢\left(\phi \wedge x=y\right)\to \left(\psi \leftrightarrow \chi \right)$$
2		eqidd	$$⊢\left(\phi \wedge x=y\right)\to A=A$$
3	1 2	cbvraldva2	$$⊢\phi \to \left(\forall x\in A\psi \leftrightarrow \forall y\in A\chi \right)$$