Definition df-symrels 38944

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 38962. Alternate definitions are dfsymrels2 38946, dfsymrels3 38947, dfsymrels4 38952 and dfsymrels5 38953.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38912) and transitive (df-trrels 38978) 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 38515	. 2 class SymRels
2		csyms 38514	. . 3 class Syms
3		crels 38506	. . 3 class Rels
4	2, 3	cin 3888	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1542	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38946