Definition df-symrels 37924

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 37938. Alternate definitions are dfsymrels2 37926, dfsymrels3 37927, dfsymrels4 37928 and dfsymrels5 37929.

This definition is similar to the definitions of the classes of reflexive (df-refrels 37892) and transitive (df-trrels 37954) 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 37565	. 2 class SymRels
2		csyms 37564	. . 3 class Syms
3		crels 37556	. . 3 class Rels
4	2, 3	cin 3942	. 2 class ( Syms ∩ Rels )
5	1, 4	wceq 1533	1 wff SymRels = ( Syms ∩ Rels )

This definition is referenced by:  dfsymrels2  37926