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Definition df-symrels 38544
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 38558. Alternate definitions are dfsymrels2 38546, dfsymrels3 38547, dfsymrels4 38548 and dfsymrels5 38549.

This definition is similar to the definitions of the classes of reflexive (df-refrels 38512) and transitive (df-trrels 38574) 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 38193 . 2 class SymRels
2 csyms 38192 . . 3 class Syms
3 crels 38184 . . 3 class Rels
42, 3cin 3950 . 2 class ( Syms ∩ Rels )
51, 4wceq 1540 1 wff SymRels = ( Syms ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfsymrels2  38546
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