Definition df-symrels 38525

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 38539. Alternate definitions are dfsymrels2 38527, dfsymrels3 38528, dfsymrels4 38529 and dfsymrels5 38530.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38493) and transitive (df-trrels 38555) 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 38173	. 2 class SymRels
2		csyms 38172	. . 3 class Syms
3		crels 38164	. . 3 class Rels
4	2, 3	cin 3962	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1537	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38527