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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 → ( 𝜑 → 𝜓 ) )
	Assertion	cbvalivw	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		cbvalivw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 → 𝜓 ) )
2	1	spimvw	⊢ ( ∀ 𝑥 𝜑 → 𝜓 )
3	2	alrimiv	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑦 𝜓 )