![]() |
Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
|
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 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.) |
Ref | Expression |
---|---|
df-symrels | ⊢ SymRels = ( Syms ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csymrels 36635 | . 2 class SymRels | |
2 | csyms 36634 | . . 3 class Syms | |
3 | crels 36626 | . . 3 class Rels | |
4 | 2, 3 | cin 3909 | . 2 class ( Syms ∩ Rels ) |
5 | 1, 4 | wceq 1541 | 1 wff SymRels = ( Syms ∩ Rels ) |
Colors of variables: wff setvar class |
This definition is referenced by: dfsymrels2 36997 |
Copyright terms: Public domain | W3C validator |