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Mirrors > Home > ILE Home > Th. List > dffo4 | Unicode version |
Description: Alternate definition of an onto mapping. (Contributed by NM, 20-Mar-2007.) |
Ref | Expression |
---|---|
dffo4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffo2 5437 |
. . 3
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2 | simpl 109 |
. . . 4
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3 | vex 2740 |
. . . . . . . . . 10
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4 | 3 | elrn 4865 |
. . . . . . . . 9
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5 | eleq2 2241 |
. . . . . . . . 9
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6 | 4, 5 | bitr3id 194 |
. . . . . . . 8
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7 | 6 | biimpar 297 |
. . . . . . 7
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8 | 7 | adantll 476 |
. . . . . 6
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9 | ffn 5360 |
. . . . . . . . . . 11
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10 | fnbr 5313 |
. . . . . . . . . . . 12
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11 | 10 | ex 115 |
. . . . . . . . . . 11
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12 | 9, 11 | syl 14 |
. . . . . . . . . 10
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13 | 12 | ancrd 326 |
. . . . . . . . 9
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14 | 13 | eximdv 1880 |
. . . . . . . 8
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15 | df-rex 2461 |
. . . . . . . 8
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16 | 14, 15 | syl6ibr 162 |
. . . . . . 7
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17 | 16 | ad2antrr 488 |
. . . . . 6
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18 | 8, 17 | mpd 13 |
. . . . 5
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19 | 18 | ralrimiva 2550 |
. . . 4
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20 | 2, 19 | jca 306 |
. . 3
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21 | 1, 20 | sylbi 121 |
. 2
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22 | fnbrfvb 5551 |
. . . . . . . . 9
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23 | 22 | biimprd 158 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | eqcom 2179 |
. . . . . . . 8
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25 | 23, 24 | syl6ib 161 |
. . . . . . 7
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26 | 9, 25 | sylan 283 |
. . . . . 6
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27 | 26 | reximdva 2579 |
. . . . 5
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28 | 27 | ralimdv 2545 |
. . . 4
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29 | 28 | imdistani 445 |
. . 3
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30 | dffo3 5658 |
. . 3
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31 | 29, 30 | sylibr 134 |
. 2
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32 | 21, 31 | impbii 126 |
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-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-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
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-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-rn 4633 df-iota 5173 df-fun 5213 df-fn 5214 df-f 5215 df-fo 5217 df-fv 5219 |
This theorem is referenced by: dffo5 5660 |
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