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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 7052 |
. . . 4
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2 | f1ofo 5467 |
. . . 4
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3 | forn 5440 |
. . . 4
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4 | 1, 2, 3 | mp2b 8 |
. . 3
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5 | djurf1or 7053 |
. . . 4
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6 | f1ofo 5467 |
. . . 4
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7 | forn 5440 |
. . . 4
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8 | 5, 6, 7 | mp2b 8 |
. . 3
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9 | 4, 8 | uneq12i 3287 |
. 2
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10 | df-dju 7034 |
. 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 4120 ax-nul 4128 ax-pow 4173 ax-pr 4208 ax-un 4432 |
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 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-mpt 4065 df-tr 4101 df-id 4292 df-iord 4365 df-on 4367 df-suc 4370 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-res 4637 df-iota 5177 df-fun 5217 df-fn 5218 df-f 5219 df-f1 5220 df-fo 5221 df-f1o 5222 df-fv 5223 df-1st 6138 df-2nd 6139 df-1o 6414 df-dju 7034 df-inl 7043 df-inr 7044 |
This theorem is referenced by: djuun 7063 eldju 7064 casedm 7082 djudm 7101 |
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