Definition df-symrels 38796

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 38814. Alternate definitions are dfsymrels2 38798, dfsymrels3 38799, dfsymrels4 38804 and dfsymrels5 38805.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38764) and transitive (df-trrels 38830) 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 38394	. 2 class SymRels
2		csyms 38393	. . 3 class Syms
3		crels 38385	. . 3 class Rels
4	2, 3	cin 3900	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1541	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  38798