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Mirrors > Home > ILE Home > Th. List > fo00 | Unicode version |
Description: Onto mapping of the empty set. (Contributed by NM, 22-Mar-2006.) |
Ref | Expression |
---|---|
fo00 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fofn 5235 |
. . . . . 6
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2 | fn0 5133 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | f10 5287 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | f1eq1 5211 |
. . . . . . . 8
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5 | 3, 4 | mpbiri 166 |
. . . . . . 7
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6 | 2, 5 | sylbi 119 |
. . . . . 6
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7 | 1, 6 | syl 14 |
. . . . 5
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8 | 7 | ancri 317 |
. . . 4
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9 | df-f1o 5022 |
. . . 4
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10 | 8, 9 | sylibr 132 |
. . 3
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11 | f1ofo 5260 |
. . 3
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12 | 10, 11 | impbii 124 |
. 2
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13 | f1o00 5288 |
. 2
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14 | 12, 13 | bitri 182 |
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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-nul 3965 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 df-opab 3900 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-fun 5017 df-fn 5018 df-f 5019 df-f1 5020 df-fo 5021 df-f1o 5022 |
This theorem is referenced by: fsumf1o 10778 |
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