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Metamath Proof Explorer

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	$⊢ ψ \to \forall x ψ$
	bj-cbv3hv2.1	$⊢ x = y \to (φ \to ψ)$
Assertion	bj-cbv3hv2	$⊢ \forall x φ \to \forall y ψ$

Proof

Step	Hyp	Ref	Expression
1		bj-cbv3hv2.nf	$⊢ ψ \to \forall x ψ$
2		bj-cbv3hv2.1	$⊢ x = y \to (φ \to ψ)$
3	1	nf5i	$⊢ Ⅎ x ψ$
4	3 2	cbv3v2	$⊢ \forall x φ \to \forall y ψ$