Definition df-symrels 39821

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 39839. Alternate definitions are dfsymrels2 39823, dfsymrels3 39824, dfsymrels4 39829 and dfsymrels5 39830.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39789) and transitive (df-trrels 39855) 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 39392	. 2 class SymRels
2		csyms 39391	. . 3 class Syms
3		crels 39383	. . 3 class Rels
4	2, 3	cin 4092	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1570	1 wff SymRels = ( Syms ∩ Rels )

This definition is used by:  dfsymrels2  39823