Definition df-symrels 35794

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 35808. Alternate definitions are dfsymrels2 35796, dfsymrels3 35797, dfsymrels4 35798 and dfsymrels5 35799.

This definition is similar to the definitions of the classes of reflexive (df-refrels 35766) and transitive (df-trrels 35824) 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 35479	. 2 class SymRels
2		csyms 35478	. . 3 class Syms
3		crels 35470	. . 3 class Rels
4	2, 3	cin 3935	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1537	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  35796