Definition df-symrels 39272

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 39290. Alternate definitions are dfsymrels2 39274, dfsymrels3 39275, dfsymrels4 39280 and dfsymrels5 39281.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39240) and transitive (df-trrels 39306) 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 38843	. 2 class SymRels
2		csyms 38842	. . 3 class Syms
3		crels 38834	. . 3 class Rels
4	2, 3	cin 3904	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1570	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  39274