Definition df-symrels 38561

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 38575. Alternate definitions are dfsymrels2 38563, dfsymrels3 38564, dfsymrels4 38565 and dfsymrels5 38566.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38529) and transitive (df-trrels 38591) 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 38210	. 2 class SymRels
2		csyms 38209	. . 3 class Syms
3		crels 38201	. . 3 class Rels
4	2, 3	cin 3925	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1540	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38563