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Mirrors > Home > ILE Home > Th. List > ssdisj | Unicode version |
Description: Intersection with a subclass of a disjoint class. (Contributed by FL, 24-Jan-2007.) |
Ref | Expression |
---|---|
ssdisj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss0b 3372 | . . . 4 | |
2 | ssrin 3271 | . . . . 5 | |
3 | sstr2 3074 | . . . . 5 | |
4 | 2, 3 | syl 14 | . . . 4 |
5 | 1, 4 | syl5bir 152 | . . 3 |
6 | 5 | imp 123 | . 2 |
7 | ss0 3373 | . 2 | |
8 | 6, 7 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 cin 3040 wss 3041 c0 3333 |
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-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 |
This theorem is referenced by: djudisj 4936 fimacnvdisj 5277 unfiin 6782 hashunlem 10518 |
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