Definition df-symrels 36351

Description: Define the class of symmetric relations. For sets, being an element of the class of symmetric relations is equivalent to satisfying the symmetric relation predicate, see elsymrelsrel 36365. Alternate definitions are dfsymrels2 36353, dfsymrels3 36354, dfsymrels4 36355 and dfsymrels5 36356.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36323) and transitive (df-trrels 36381) relations. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion

Ref	Expression
df-symrels	⊢ SymRels = ( Syms ∩ Rels )

Detailed syntax breakdown of Definition df-symrels

Step	Hyp	Ref	Expression
1		csymrels 36038	. 2 class SymRels
2		csyms 36037	. . 3 class Syms
3		crels 36029	. . 3 class Rels
4	2, 3	cin 3856	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1543	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  36353