Definition df-symrels 38534

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 38548. Alternate definitions are dfsymrels2 38536, dfsymrels3 38537, dfsymrels4 38538 and dfsymrels5 38539.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38502) and transitive (df-trrels 38564) 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 38180	. 2 class SymRels
2		csyms 38179	. . 3 class Syms
3		crels 38171	. . 3 class Rels
4	2, 3	cin 3913	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1540	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38536