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Mirrors > Home > ILE Home > Th. List > mpt20 | Unicode version |
Description: A mapping operation with empty domain. (Contributed by Stefan O'Rear, 29-Jan-2015.) (Revised by Mario Carneiro, 15-May-2015.) |
Ref | Expression |
---|---|
mpt20 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt2 5517 | . 2 | |
2 | df-oprab 5516 | . 2 | |
3 | noel 3228 | . . . . . . 7 | |
4 | simprll 489 | . . . . . . 7 | |
5 | 3, 4 | mto 588 | . . . . . 6 |
6 | 5 | nex 1389 | . . . . 5 |
7 | 6 | nex 1389 | . . . 4 |
8 | 7 | nex 1389 | . . 3 |
9 | 8 | abf 3260 | . 2 |
10 | 1, 2, 9 | 3eqtri 2064 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wex 1381 wcel 1393 cab 2026 c0 3224 cop 3378 coprab 5513 cmpt2 5514 |
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-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-in 2924 df-ss 2931 df-nul 3225 df-oprab 5516 df-mpt2 5517 |
This theorem is referenced by: (None) |
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