Definition df-symrels 39371

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 39389. Alternate definitions are dfsymrels2 39373, dfsymrels3 39374, dfsymrels4 39379 and dfsymrels5 39380.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39339) and transitive (df-trrels 39405) 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 38942	. 2 class SymRels
2		csyms 38941	. . 3 class Syms
3		crels 38933	. . 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  39373