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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 2423 | . . 3 | |
2 | df-rab 2423 | . . 3 | |
3 | 1, 2 | difeq12i 3187 | . 2 |
4 | df-rab 2423 | . . 3 | |
5 | difab 3340 | . . . 4 | |
6 | anass 398 | . . . . . 6 | |
7 | simpr 109 | . . . . . . . . 9 | |
8 | 7 | con3i 621 | . . . . . . . 8 |
9 | 8 | anim2i 339 | . . . . . . 7 |
10 | pm3.2 138 | . . . . . . . . . 10 | |
11 | 10 | adantr 274 | . . . . . . . . 9 |
12 | 11 | con3d 620 | . . . . . . . 8 |
13 | 12 | imdistani 441 | . . . . . . 7 |
14 | 9, 13 | impbii 125 | . . . . . 6 |
15 | 6, 14 | bitr3i 185 | . . . . 5 |
16 | 15 | abbii 2253 | . . . 4 |
17 | 5, 16 | eqtr4i 2161 | . . 3 |
18 | 4, 17 | eqtr4i 2161 | . 2 |
19 | 3, 18 | eqtr4i 2161 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1331 wcel 1480 cab 2123 crab 2418 cdif 3063 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rab 2423 df-v 2683 df-dif 3068 |
This theorem is referenced by: (None) |
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