Theorem issettru

Description: Weak version of isset . (Contributed by BJ, 24-Apr-2024)

	Ref	Expression
Assertion	issettru	$$⊢\exists xx=A\leftrightarrow A\in \left\{y|\top \right\}$$

Proof

Step	Hyp	Ref	Expression
1		vextru	$$⊢x\in \left\{y|\top \right\}$$
2	1	biantru	$$⊢x=A\leftrightarrow \left(x=A\wedge x\in \left\{y|\top \right\}\right)$$
3	2	exbii	$$⊢\exists xx=A\leftrightarrow \exists x\left(x=A\wedge x\in \left\{y|\top \right\}\right)$$
4		dfclel	$$⊢A\in \left\{y|\top \right\}\leftrightarrow \exists x\left(x=A\wedge x\in \left\{y|\top \right\}\right)$$
5	3 4	bitr4i	$$⊢\exists xx=A\leftrightarrow A\in \left\{y|\top \right\}$$