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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 2357 | . . 3 | |
2 | df-rab 2357 | . . 3 | |
3 | 1, 2 | difeq12i 3088 | . 2 |
4 | df-rab 2357 | . . 3 | |
5 | difab 3233 | . . . 4 | |
6 | anass 393 | . . . . . 6 | |
7 | simpr 108 | . . . . . . . . 9 | |
8 | 7 | con3i 594 | . . . . . . . 8 |
9 | 8 | anim2i 334 | . . . . . . 7 |
10 | pm3.2 137 | . . . . . . . . . 10 | |
11 | 10 | adantr 270 | . . . . . . . . 9 |
12 | 11 | con3d 593 | . . . . . . . 8 |
13 | 12 | imdistani 433 | . . . . . . 7 |
14 | 9, 13 | impbii 124 | . . . . . 6 |
15 | 6, 14 | bitr3i 184 | . . . . 5 |
16 | 15 | abbii 2194 | . . . 4 |
17 | 5, 16 | eqtr4i 2104 | . . 3 |
18 | 4, 17 | eqtr4i 2104 | . 2 |
19 | 3, 18 | eqtr4i 2104 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wceq 1284 wcel 1433 cab 2067 crab 2352 cdif 2970 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rab 2357 df-v 2603 df-dif 2975 |
This theorem is referenced by: (None) |
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