This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Define the class of all transitive sets. (Contributed by Scott Fenton, 31-Mar-2012)
|
|
Ref |
Expression |
|
Assertion |
df-trans |
⊢ Trans = ( V ∖ ran ( ( E ∘ E ) ∖ E ) ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
ctrans |
⊢ Trans |
| 1 |
|
cvv |
⊢ V |
| 2 |
|
cep |
⊢ E |
| 3 |
2 2
|
ccom |
⊢ ( E ∘ E ) |
| 4 |
3 2
|
cdif |
⊢ ( ( E ∘ E ) ∖ E ) |
| 5 |
4
|
crn |
⊢ ran ( ( E ∘ E ) ∖ E ) |
| 6 |
1 5
|
cdif |
⊢ ( V ∖ ran ( ( E ∘ E ) ∖ E ) ) |
| 7 |
0 6
|
wceq |
⊢ Trans = ( V ∖ ran ( ( E ∘ E ) ∖ E ) ) |