Theorem bj-cbv3hv2

Description: Version of cbv3h with two disjoint variable conditions, which does not require ax-11 nor ax-13 . (Contributed by BJ, 24-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-cbv3hv2.nf	$$⊢\psi \to \forall x\psi$$
	bj-cbv3hv2.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	bj-cbv3hv2	$$⊢\forall x\phi \to \forall y\psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-cbv3hv2.nf	$$⊢\psi \to \forall x\psi$$
2		bj-cbv3hv2.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
3	1	nf5i	$$⊢Ⅎx\psi$$
4	3 2	cbv3v2	$$⊢\forall x\phi \to \forall y\psi$$