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Metamath Proof Explorer

Theorem inteqi

Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003)

		Ref	Expression
	Hypothesis	inteqi.1	$⊢ A = B$
	Assertion	inteqi	$⊢ ⋂ A = ⋂ B$

Step	Hyp	Ref	Expression
1		inteqi.1	$⊢ A = B$
2		inteq	$⊢ A = B \to ⋂ A = ⋂ B$
3	1 2	ax-mp	$⊢ ⋂ A = ⋂ B$