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Metamath Proof Explorer

Theorem ec0

Description: The empty-coset of a class is the empty set. (Contributed by Peter Mazsa, 19-May-2019)

		Ref	Expression
	Assertion	ec0	$⊢ [A] \emptyset = \emptyset$

Step	Hyp	Ref	Expression
1		df-ec	$⊢ [A] \emptyset = \emptyset [\{A\}]$
2		0ima	$⊢ \emptyset [\{A\}] = \emptyset$
3	1 2	eqtri	$⊢ [A] \emptyset = \emptyset$