Definition df-symrels 39662

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 39680. Alternate definitions are dfsymrels2 39664, dfsymrels3 39665, dfsymrels4 39670 and dfsymrels5 39671.

This definition is similar to the definitions of the classes of reflexive (df-refrels 39630) and transitive (df-trrels 39696) 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 39233	. 2 class SymRels
2		csyms 39232	. . 3 class Syms
3		crels 39224	. . 3 class Rels
4	2, 3	cin 4088	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1569	1 wff SymRels = ( Syms ∩ Rels )

This definition is used by:  dfsymrels2  39664