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Metamath Proof Explorer

Theorem modom2

Description: Two ways to express "at most one". (Contributed by Mario Carneiro, 24-Dec-2016)

		Ref	Expression
	Assertion	modom2	$⊢ \exists^{*} x x \in A \leftrightarrow A ≼ 1_{𝑜}$

Step	Hyp	Ref	Expression
1		modom	$⊢ \exists^{*} x x \in A \leftrightarrow \{x \| x \in A\} ≼ 1_{𝑜}$
2		abid2	$⊢ \{x \| x \in A\} = A$
3	2	breq1i	$⊢ \{x \| x \in A\} ≼ 1_{𝑜} \leftrightarrow A ≼ 1_{𝑜}$
4	1 3	bitri	$⊢ \exists^{*} x x \in A \leftrightarrow A ≼ 1_{𝑜}$