Definition df-symrels 38990

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 39008. Alternate definitions are dfsymrels2 38992, dfsymrels3 38993, dfsymrels4 38998 and dfsymrels5 38999.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38958) and transitive (df-trrels 39024) 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 38561	. 2 class SymRels
2		csyms 38560	. . 3 class Syms
3		crels 38552	. . 3 class Rels
4	2, 3	cin 3882	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1547	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38992