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Metamath Proof Explorer

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	$⊢ x = y \to (φ \to ψ)$
	Assertion	cbvalivw	$⊢ \forall x φ \to \forall y ψ$

Proof

Step	Hyp	Ref	Expression
1		cbvalivw.1	$⊢ x = y \to (φ \to ψ)$
2	1	spimvw	$⊢ \forall x φ \to ψ$
3	2	alrimiv	$⊢ \forall x φ \to \forall y ψ$