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Metamath Proof Explorer

Theorem hbaev

Description: All variables are effectively bound in an identical variable specifier. Version of hbae with a disjoint variable condition, requiring fewer axioms. Instance of aev2 . (Contributed by NM, 13-May-1993) Reduce axiom usage. (Revised by Wolf Lammen, 22-Mar-2021)

		Ref	Expression
	Assertion	hbaev	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ∀ 𝑥 𝑥 = 𝑦 )

Proof

Step	Hyp	Ref	Expression
1		aev2	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ∀ 𝑧 ∀ 𝑥 𝑥 = 𝑦 )