Definition df-symrels 39305

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 39323. Alternate definitions are dfsymrels2 39307, dfsymrels3 39308, dfsymrels4 39313 and dfsymrels5 39314.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39273) and transitive (df-trrels 39339) 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 38876	. 2 class SymRels
2		csyms 38875	. . 3 class Syms
3		crels 38867	. . 3 class Rels
4	2, 3	cin 3905	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1570	1 wff SymRels = ( Syms ∩ Rels )

This definition is used by:  dfsymrels2  39307