Definition df-symrels 38586

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 38600. Alternate definitions are dfsymrels2 38588, dfsymrels3 38589, dfsymrels4 38590 and dfsymrels5 38591.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38554) and transitive (df-trrels 38616) 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 38232	. 2 class SymRels
2		csyms 38231	. . 3 class Syms
3		crels 38223	. . 3 class Rels
4	2, 3	cin 3901	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1541	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38588