Definition df-symrels 38544

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 38558. Alternate definitions are dfsymrels2 38546, dfsymrels3 38547, dfsymrels4 38548 and dfsymrels5 38549.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38512) and transitive (df-trrels 38574) 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 38193	. 2 class SymRels
2		csyms 38192	. . 3 class Syms
3		crels 38184	. . 3 class Rels
4	2, 3	cin 3950	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1540	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38546