Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > limeq | Unicode version |
Description: Equality theorem for the limit predicate. (Contributed by NM, 22-Apr-1994.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
limeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordeq 4332 | . . 3 | |
2 | eleq2 2221 | . . 3 | |
3 | id 19 | . . . 4 | |
4 | unieq 3781 | . . . 4 | |
5 | 3, 4 | eqeq12d 2172 | . . 3 |
6 | 1, 2, 5 | 3anbi123d 1294 | . 2 |
7 | dflim2 4330 | . 2 | |
8 | dflim2 4330 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 963 wceq 1335 wcel 2128 c0 3394 cuni 3772 word 4322 wlim 4324 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-in 3108 df-ss 3115 df-uni 3773 df-tr 4063 df-iord 4326 df-ilim 4329 |
This theorem is referenced by: limuni2 4357 |
Copyright terms: Public domain | W3C validator |