Mathbox for David A. Wheeler |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-irreflexive | Structured version Visualization version Unicode version |
Description: Define irreflexive relation; relation is irreflexive over the set iff . Note that a relation can be neither reflexive nor irreflexive. (Contributed by David A. Wheeler, 1-Dec-2019.) |
Ref | Expression |
---|---|
df-irreflexive | Irreflexive |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | cR | . . 3 | |
3 | 1, 2 | wirreflexive 42510 | . 2 Irreflexive |
4 | 1, 1 | cxp 5112 | . . . 4 |
5 | 2, 4 | wss 3574 | . . 3 |
6 | vx | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | 7, 7, 2 | wbr 4653 | . . . . 5 |
9 | 8 | wn 3 | . . . 4 |
10 | 9, 6, 1 | wral 2912 | . . 3 |
11 | 5, 10 | wa 384 | . 2 |
12 | 3, 11 | wb 196 | 1 Irreflexive |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
Copyright terms: Public domain | W3C validator |