![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > onordi | GIF version |
Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994.) |
Ref | Expression |
---|---|
on.1 | ⊢ A ∈ On |
Ref | Expression |
---|---|
onordi | ⊢ Ord A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 | . 2 ⊢ A ∈ On | |
2 | eloni 4078 | . 2 ⊢ (A ∈ On → Ord A) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ Ord A |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1390 Ord word 4065 Oncon0 4066 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 df-v 2553 df-in 2918 df-ss 2925 df-uni 3572 df-tr 3846 df-iord 4069 df-on 4071 |
This theorem is referenced by: ontrci 4130 onsucsssucexmid 4212 |
Copyright terms: Public domain | W3C validator |