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Metamath Proof Explorer

Theorem eqeng

Description: Equality implies equinumerosity. (Contributed by NM, 26-Oct-2003)

		Ref	Expression
	Assertion	eqeng	$⊢ A \in V \to (A = B \to A \approx B)$

Step	Hyp	Ref	Expression
1		enrefg	$⊢ A \in V \to A \approx A$
2		breq2	$⊢ A = B \to (A \approx A \leftrightarrow A \approx B)$
3	1 2	syl5ibcom	$⊢ A \in V \to (A = B \to A \approx B)$