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Mirrors > Home > ILE Home > Th. List > djuunr | Unicode version |
Description: The disjoint union of two classes is the union of the images of those two classes under right and left injection. (Contributed by Jim Kingdon, 22-Jun-2022.) (Proof shortened by BJ, 6-Jul-2022.) |
Ref | Expression |
---|---|
djuunr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | djulf1or 7055 |
. . . 4
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2 | f1ofo 5469 |
. . . 4
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3 | forn 5442 |
. . . 4
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4 | 1, 2, 3 | mp2b 8 |
. . 3
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5 | djurf1or 7056 |
. . . 4
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6 | f1ofo 5469 |
. . . 4
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7 | forn 5442 |
. . . 4
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8 | 5, 6, 7 | mp2b 8 |
. . 3
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9 | 4, 8 | uneq12i 3288 |
. 2
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10 | df-dju 7037 |
. 2
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11 | 9, 10 | eqtr4i 2201 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4122 ax-nul 4130 ax-pow 4175 ax-pr 4210 ax-un 4434 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2740 df-sbc 2964 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-nul 3424 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-opab 4066 df-mpt 4067 df-tr 4103 df-id 4294 df-iord 4367 df-on 4369 df-suc 4372 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-f1 5222 df-fo 5223 df-f1o 5224 df-fv 5225 df-1st 6141 df-2nd 6142 df-1o 6417 df-dju 7037 df-inl 7046 df-inr 7047 |
This theorem is referenced by: djuun 7066 eldju 7067 casedm 7085 djudm 7104 |
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