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Mirrors > Home > ILE Home > Th. List > iotaeq | Unicode version |
Description: Equality theorem for descriptions. (Contributed by Andrew Salmon, 30-Jun-2011.) |
Ref | Expression |
---|---|
iotaeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | drsb1 1779 | . . . . . . 7 | |
2 | df-clab 2144 | . . . . . . 7 | |
3 | df-clab 2144 | . . . . . . 7 | |
4 | 1, 2, 3 | 3bitr4g 222 | . . . . . 6 |
5 | 4 | eqrdv 2155 | . . . . 5 |
6 | 5 | eqeq1d 2166 | . . . 4 |
7 | 6 | abbidv 2275 | . . 3 |
8 | 7 | unieqd 3783 | . 2 |
9 | df-iota 5135 | . 2 | |
10 | df-iota 5135 | . 2 | |
11 | 8, 9, 10 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1333 wceq 1335 wsb 1742 wcel 2128 cab 2143 csn 3560 cuni 3772 cio 5133 |
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-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-uni 3773 df-iota 5135 |
This theorem is referenced by: (None) |
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