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Mirrors > Home > ILE Home > Th. List > disj | Unicode version |
Description: Two ways of saying that two classes are disjoint (have no members in common). (Contributed by NM, 17-Feb-2004.) |
Ref | Expression |
---|---|
disj |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-in 2918 |
. . . 4
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2 | 1 | eqeq1i 2044 |
. . 3
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3 | abeq1 2144 |
. . 3
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4 | imnan 623 |
. . . . 5
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5 | noel 3222 |
. . . . . 6
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6 | 5 | nbn 614 |
. . . . 5
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7 | 4, 6 | bitr2i 174 |
. . . 4
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8 | 7 | albii 1356 |
. . 3
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9 | 2, 3, 8 | 3bitri 195 |
. 2
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10 | df-ral 2305 |
. 2
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11 | 9, 10 | bitr4i 176 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-v 2553 df-dif 2914 df-in 2918 df-nul 3219 |
This theorem is referenced by: disjr 3263 disj1 3264 disjne 3267 renfdisj 6876 |
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