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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 2402 | . . 3 | |
2 | df-rab 2402 | . . 3 | |
3 | 1, 2 | difeq12i 3162 | . 2 |
4 | df-rab 2402 | . . 3 | |
5 | difab 3315 | . . . 4 | |
6 | anass 398 | . . . . . 6 | |
7 | simpr 109 | . . . . . . . . 9 | |
8 | 7 | con3i 606 | . . . . . . . 8 |
9 | 8 | anim2i 339 | . . . . . . 7 |
10 | pm3.2 138 | . . . . . . . . . 10 | |
11 | 10 | adantr 274 | . . . . . . . . 9 |
12 | 11 | con3d 605 | . . . . . . . 8 |
13 | 12 | imdistani 441 | . . . . . . 7 |
14 | 9, 13 | impbii 125 | . . . . . 6 |
15 | 6, 14 | bitr3i 185 | . . . . 5 |
16 | 15 | abbii 2233 | . . . 4 |
17 | 5, 16 | eqtr4i 2141 | . . 3 |
18 | 4, 17 | eqtr4i 2141 | . 2 |
19 | 3, 18 | eqtr4i 2141 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1316 wcel 1465 cab 2103 crab 2397 cdif 3038 |
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-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rab 2402 df-v 2662 df-dif 3043 |
This theorem is referenced by: (None) |
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