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Mirrors > Home > ILE Home > Th. List > difrab | Unicode version |
Description: Difference of two restricted class abstractions. (Contributed by NM, 23-Oct-2004.) |
Ref | Expression |
---|---|
difrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2315 | . . 3 | |
2 | df-rab 2315 | . . 3 | |
3 | 1, 2 | difeq12i 3060 | . 2 |
4 | df-rab 2315 | . . 3 | |
5 | difab 3206 | . . . 4 | |
6 | anass 381 | . . . . . 6 | |
7 | simpr 103 | . . . . . . . . 9 | |
8 | 7 | con3i 562 | . . . . . . . 8 |
9 | 8 | anim2i 324 | . . . . . . 7 |
10 | pm3.2 126 | . . . . . . . . . 10 | |
11 | 10 | adantr 261 | . . . . . . . . 9 |
12 | 11 | con3d 561 | . . . . . . . 8 |
13 | 12 | imdistani 419 | . . . . . . 7 |
14 | 9, 13 | impbii 117 | . . . . . 6 |
15 | 6, 14 | bitr3i 175 | . . . . 5 |
16 | 15 | abbii 2153 | . . . 4 |
17 | 5, 16 | eqtr4i 2063 | . . 3 |
18 | 4, 17 | eqtr4i 2063 | . 2 |
19 | 3, 18 | eqtr4i 2063 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wcel 1393 cab 2026 crab 2310 cdif 2914 |
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-ral 2311 df-rab 2315 df-v 2559 df-dif 2920 |
This theorem is referenced by: (None) |
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