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Mirrors > Home > ILE Home > Th. List > dfco2a | Unicode version |
Description: Generalization of dfco2 5128, where ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dfco2a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfco2 5128 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | vex 2740 |
. . . . . . . . . . . . . 14
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3 | vex 2740 |
. . . . . . . . . . . . . . 15
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4 | 3 | eliniseg 4998 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | ax-mp 5 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 3, 2 | brelrn 4860 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 5, 6 | sylbi 121 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | vex 2740 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() | |
9 | 2, 8 | elimasn 4995 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 2, 8 | opeldm 4830 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 9, 10 | sylbi 121 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 7, 11 | anim12ci 339 |
. . . . . . . . . . 11
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13 | 12 | adantl 277 |
. . . . . . . . . 10
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14 | 13 | exlimivv 1896 |
. . . . . . . . 9
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15 | elxp 4643 |
. . . . . . . . 9
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16 | elin 3318 |
. . . . . . . . 9
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17 | 14, 15, 16 | 3imtr4i 201 |
. . . . . . . 8
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18 | ssel 3149 |
. . . . . . . 8
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19 | 17, 18 | syl5 32 |
. . . . . . 7
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20 | 19 | pm4.71rd 394 |
. . . . . 6
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21 | 20 | exbidv 1825 |
. . . . 5
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22 | rexv 2755 |
. . . . 5
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23 | df-rex 2461 |
. . . . 5
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24 | 21, 22, 23 | 3bitr4g 223 |
. . . 4
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25 | eliun 3890 |
. . . 4
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26 | eliun 3890 |
. . . 4
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27 | 24, 25, 26 | 3bitr4g 223 |
. . 3
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28 | 27 | eqrdv 2175 |
. 2
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29 | 1, 28 | eqtrid 2222 |
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 4121 ax-pow 4174 ax-pr 4209 |
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 3577 df-sn 3598 df-pr 3599 df-op 3601 df-iun 3888 df-br 4004 df-opab 4065 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 |
This theorem is referenced by: (None) |
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