Definition df-symrels 38935

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 38953. Alternate definitions are dfsymrels2 38937, dfsymrels3 38938, dfsymrels4 38943 and dfsymrels5 38944.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38903) and transitive (df-trrels 38969) 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 38506	. 2 class SymRels
2		csyms 38505	. . 3 class Syms
3		crels 38497	. . 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  38937