Definition df-symrels 38958

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 38976. Alternate definitions are dfsymrels2 38960, dfsymrels3 38961, dfsymrels4 38966 and dfsymrels5 38967.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38926) and transitive (df-trrels 38992) 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 38529	. 2 class SymRels
2		csyms 38528	. . 3 class Syms
3		crels 38520	. . 3 class Rels
4	2, 3	cin 3889	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1542	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38960