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	|- ( R Reflexive A <-> ( R C_ ( A X. A ) /\ A. x e. A x R x ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cR	|- R
1		cA	|- A
2	1 0	wreflexive	|- R Reflexive A
3	1 1	cxp	|- ( A X. A )
4	0 3	wss	|- R C_ ( A X. A )
5		vx	|- x
6	5	cv	|- x
7	6 6 0	wbr	|- x R x
8	7 5 1	wral	|- A. x e. A x R x
9	4 8	wa	|- ( R C_ ( A X. A ) /\ A. x e. A x R x )
10	2 9	wb	|- ( R Reflexive A <-> ( R C_ ( A X. A ) /\ A. x e. A x R x ) )