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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 4357 | . . 3 | |
2 | eleq2 2234 | . . 3 | |
3 | id 19 | . . . 4 | |
4 | unieq 3805 | . . . 4 | |
5 | 3, 4 | eqeq12d 2185 | . . 3 |
6 | 1, 2, 5 | 3anbi123d 1307 | . 2 |
7 | dflim2 4355 | . 2 | |
8 | dflim2 4355 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 973 wceq 1348 wcel 2141 c0 3414 cuni 3796 word 4347 wlim 4349 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-in 3127 df-ss 3134 df-uni 3797 df-tr 4088 df-iord 4351 df-ilim 4354 |
This theorem is referenced by: limuni2 4382 |
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