Definition df-symrels 38658

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 38676. Alternate definitions are dfsymrels2 38660, dfsymrels3 38661, dfsymrels4 38666 and dfsymrels5 38667.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38626) and transitive (df-trrels 38692) 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 38256	. 2 class SymRels
2		csyms 38255	. . 3 class Syms
3		crels 38247	. . 3 class Rels
4	2, 3	cin 3897	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1541	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38660