Theorem issetf

Description: A version of isset that does not require x and A to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011) (Revised by Mario Carneiro, 10-Oct-2016)

	Ref	Expression
Hypothesis	issetf.1	$$⊢\underset{\_}{Ⅎ}xA$$
Assertion	issetf	$$⊢A\in \mathrm{V}\leftrightarrow \exists xx=A$$

Proof

Step	Hyp	Ref	Expression
1		issetf.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		issetft	$$⊢\underset{\_}{Ⅎ}xA\to \left(A\in \mathrm{V}\leftrightarrow \exists xx=A\right)$$
3	1 2	ax-mp	$$⊢A\in \mathrm{V}\leftrightarrow \exists xx=A$$