Theorem cbvalivw

Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of KalishMontague p. 86. (Contributed by NM, 9-Apr-2017)

	Ref	Expression
Hypothesis	cbvalivw.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	cbvalivw	$$⊢\forall x\phi \to \forall y\psi$$

Proof

Step	Hyp	Ref	Expression
1		cbvalivw.1	$$⊢x=y\to \left(\phi \to \psi \right)$$
2	1	spimvw	$$⊢\forall x\phi \to \psi$$
3	2	alrimiv	$$⊢\forall x\phi \to \forall y\psi$$