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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 5459 |
. . . . . 6
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2 | fn0 5354 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | f10 5514 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
4 | f1eq1 5435 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | mpbiri 168 |
. . . . . . 7
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6 | 2, 5 | sylbi 121 |
. . . . . 6
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7 | 1, 6 | syl 14 |
. . . . 5
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8 | 7 | ancri 324 |
. . . 4
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9 | df-f1o 5242 |
. . . 4
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10 | 8, 9 | sylibr 134 |
. . 3
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11 | f1ofo 5487 |
. . 3
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12 | 10, 11 | impbii 126 |
. 2
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13 | f1o00 5515 |
. 2
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14 | 12, 13 | bitri 184 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 |
This theorem is referenced by: enumct 7145 fsumf1o 11433 fprodf1o 11631 |
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