Definition df-symrels 38522

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 38536. Alternate definitions are dfsymrels2 38524, dfsymrels3 38525, dfsymrels4 38526 and dfsymrels5 38527.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38490) and transitive (df-trrels 38552) 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 38168	. 2 class SymRels
2		csyms 38167	. . 3 class Syms
3		crels 38159	. . 3 class Rels
4	2, 3	cin 3904	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1540	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38524