Definition df-symrels 38047

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 38061. Alternate definitions are dfsymrels2 38049, dfsymrels3 38050, dfsymrels4 38051 and dfsymrels5 38052.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38015) and transitive (df-trrels 38077) 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 37692	. 2 class SymRels
2		csyms 37691	. . 3 class Syms
3		crels 37683	. . 3 class Rels
4	2, 3	cin 3948	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1533	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38049