Definition df-symrels 38499

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 38513. Alternate definitions are dfsymrels2 38501, dfsymrels3 38502, dfsymrels4 38503 and dfsymrels5 38504.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38467) and transitive (df-trrels 38529) 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 38146	. 2 class SymRels
2		csyms 38145	. . 3 class Syms
3		crels 38137	. . 3 class Rels
4	2, 3	cin 3975	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1537	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38501