Theorem cbv3v2

Description: Version of cbv3 with two disjoint variable conditions, which does not require ax-11 nor ax-13 . (Contributed by BJ, 24-Jun-2019) (Proof shortened by Wolf Lammen, 30-Aug-2021)

	Ref	Expression
Hypotheses	cbv3v2.nf	$$⊢Ⅎx\psi$$
	cbv3v2.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	cbv3v2	$$⊢\forall x\phi \to \forall y\psi$$

Proof

Step	Hyp	Ref	Expression
1		cbv3v2.nf	$$⊢Ⅎx\psi$$
2		cbv3v2.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
3	1 2	spimfv	$$⊢\forall x\phi \to \psi$$
4	3	alrimiv	$$⊢\forall x\phi \to \forall y\psi$$