Definition df-symrels 37408

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 37422. Alternate definitions are dfsymrels2 37410, dfsymrels3 37411, dfsymrels4 37412 and dfsymrels5 37413.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37376) and transitive (df-trrels 37438) 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 37049	. 2 class SymRels
2		csyms 37048	. . 3 class Syms
3		crels 37040	. . 3 class Rels
4	2, 3	cin 3947	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1541	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  37410