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Mirrors > Home > ILE Home > Th. List > difdif | Unicode version |
Description: Double class difference. Exercise 11 of [TakeutiZaring] p. 22. (Contributed by NM, 17-May-1998.) |
Ref | Expression |
---|---|
difdif |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 102 | . . 3 | |
2 | pm4.45im 317 | . . . 4 | |
3 | imanim 785 | . . . . . 6 | |
4 | eldif 2927 | . . . . . 6 | |
5 | 3, 4 | sylnibr 602 | . . . . 5 |
6 | 5 | anim2i 324 | . . . 4 |
7 | 2, 6 | sylbi 114 | . . 3 |
8 | 1, 7 | impbii 117 | . 2 |
9 | 8 | difeqri 3064 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wcel 1393 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-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 |
This theorem is referenced by: dif0 3294 |
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