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Definition df-symrels 36995
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 37009. Alternate definitions are dfsymrels2 36997, dfsymrels3 36998, dfsymrels4 36999 and dfsymrels5 37000.

This definition is similar to the definitions of the classes of reflexive (df-refrels 36963) and transitive (df-trrels 37025) relations. (Contributed by Peter Mazsa, 7-Jul-2019.)

Assertion
Ref Expression
df-symrels SymRels = ( Syms ∩ Rels )

Detailed syntax breakdown of Definition df-symrels
StepHypRef Expression
1 csymrels 36635 . 2 class SymRels
2 csyms 36634 . . 3 class Syms
3 crels 36626 . . 3 class Rels
42, 3cin 3909 . 2 class ( Syms ∩ Rels )
51, 4wceq 1541 1 wff SymRels = ( Syms ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfsymrels2  36997
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