![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-er | Unicode version |
Description: Define the equivalence relation predicate. Our notation is not standard. A formal notation doesn't seem to exist in the literature; instead only informal English tends to be used. The present definition, although somewhat cryptic, nicely avoids dummy variables. In dfer2 6530 we derive a more typical definition. We show that an equivalence relation is reflexive, symmetric, and transitive in erref 6549, ersymb 6543, and ertr 6544. (Contributed by NM, 4-Jun-1995.) (Revised by Mario Carneiro, 2-Nov-2015.) |
Ref | Expression |
---|---|
df-er |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . 3
![]() ![]() | |
2 | cR |
. . 3
![]() ![]() | |
3 | 1, 2 | wer 6526 |
. 2
![]() ![]() ![]() ![]() |
4 | 2 | wrel 4628 |
. . 3
![]() ![]() ![]() |
5 | 2 | cdm 4623 |
. . . 4
![]() ![]() ![]() |
6 | 5, 1 | wceq 1353 |
. . 3
![]() ![]() ![]() ![]() ![]() |
7 | 2 | ccnv 4622 |
. . . . 5
![]() ![]() ![]() |
8 | 2, 2 | ccom 4627 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
9 | 7, 8 | cun 3127 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 9, 2 | wss 3129 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 4, 6, 10 | w3a 978 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 3, 11 | wb 105 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: dfer2 6530 ereq1 6536 ereq2 6537 errel 6538 erdm 6539 ersym 6541 ertr 6544 xpider 6600 |
Copyright terms: Public domain | W3C validator |