Definition df-symrels 38541

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 38555. Alternate definitions are dfsymrels2 38543, dfsymrels3 38544, dfsymrels4 38545 and dfsymrels5 38546.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38509) and transitive (df-trrels 38571) 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 38187	. 2 class SymRels
2		csyms 38186	. . 3 class Syms
3		crels 38178	. . 3 class Rels
4	2, 3	cin 3916	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1540	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38543