Definition df-symrels 39083

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 39101. Alternate definitions are dfsymrels2 39085, dfsymrels3 39086, dfsymrels4 39091 and dfsymrels5 39092.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39051) and transitive (df-trrels 39117) 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 38654	. 2 class SymRels
2		csyms 38653	. . 3 class Syms
3		crels 38645	. . 3 class Rels
4	2, 3	cin 3901	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1559	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  39085