Definition df-reflexive

Description: Define reflexive relation; relation R is reflexive over the set A iff A. x e. A x R x . (Contributed by David A. Wheeler, 1-Dec-2019)

	Ref	Expression
Assertion	df-reflexive	$$⊢RReflexiveA\leftrightarrow \left(R\subseteq A\times A\wedge \forall x\in AxRx\right)$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cR	$$classR$$
1		cA	$$classA$$
2	1 0	wreflexive	$$wffRReflexiveA$$
3	1 1	cxp	$$class\left(A\times A\right)$$
4	0 3	wss	$$wffR\subseteq A\times A$$
5		vx	$$setvarx$$
6	5	cv	$$setvarx$$
7	6 6 0	wbr	$$wffxRx$$
8	7 5 1	wral	$$wff\forall x\in AxRx$$
9	4 8	wa	$$wff\left(R\subseteq A\times A\wedge \forall x\in AxRx\right)$$
10	2 9	wb	$$wff\left(RReflexiveA\leftrightarrow \left(R\subseteq A\times A\wedge \forall x\in AxRx\right)\right)$$