Theorem modom2

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

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

Proof

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