Definition df-symrels 38871

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 38889. Alternate definitions are dfsymrels2 38873, dfsymrels3 38874, dfsymrels4 38879 and dfsymrels5 38880.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38839) and transitive (df-trrels 38905) 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 38442	. 2 class SymRels
2		csyms 38441	. . 3 class Syms
3		crels 38433	. . 3 class Rels
4	2, 3	cin 3902	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1542	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38873