Definition df-symrels 39535

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 39553. Alternate definitions are dfsymrels2 39537, dfsymrels3 39538, dfsymrels4 39543 and dfsymrels5 39544.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39503) and transitive (df-trrels 39569) 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 39106	. 2 class SymRels
2		csyms 39105	. . 3 class Syms
3		crels 39097	. . 3 class Rels
4	2, 3	cin 3898	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1570	1 wff SymRels = ( Syms ∩ Rels )

This definition is used by:  dfsymrels2  39537