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Mirrors > Home > ILE Home > Th. List > disjr | Unicode version |
Description: Two ways of saying that two classes are disjoint. (Contributed by Jeff Madsen, 19-Jun-2011.) |
Ref | Expression |
---|---|
disjr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom 3299 | . . 3 | |
2 | 1 | eqeq1i 2165 | . 2 |
3 | disj 3442 | . 2 | |
4 | 2, 3 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wceq 1335 wcel 2128 wral 2435 cin 3101 c0 3394 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-dif 3104 df-in 3108 df-nul 3395 |
This theorem is referenced by: (None) |
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