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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-symrels | Structured version Visualization version GIF version |
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 36365. Alternate definitions are
dfsymrels2 36353, dfsymrels3 36354, dfsymrels4 36355 and dfsymrels5 36356.
This definition is similar to the definitions of the classes of reflexive (df-refrels 36323) and transitive (df-trrels 36381) relations. (Contributed by Peter Mazsa, 7-Jul-2019.) |
Ref | Expression |
---|---|
df-symrels | ⊢ SymRels = ( Syms ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csymrels 36038 | . 2 class SymRels | |
2 | csyms 36037 | . . 3 class Syms | |
3 | crels 36029 | . . 3 class Rels | |
4 | 2, 3 | cin 3856 | . 2 class ( Syms ∩ Rels ) |
5 | 1, 4 | wceq 1543 | 1 wff SymRels = ( Syms ∩ Rels ) |
Colors of variables: wff setvar class |
This definition is referenced by: dfsymrels2 36353 |
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