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Mirrors > Home > ILE Home > Th. List > ctssdclemr | Unicode version |
Description: Lemma for ctssdc 7111. Showing that our usual definition of countable implies the alternate one. (Contributed by Jim Kingdon, 16-Aug-2023.) |
Ref | Expression |
---|---|
ctssdclemr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | foeq1 5434 |
. . 3
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2 | 1 | cbvexv 1918 |
. 2
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3 | id 19 |
. . . . . 6
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4 | eqid 2177 |
. . . . . 6
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5 | eqid 2177 |
. . . . . 6
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6 | 3, 4, 5 | ctssdccl 7109 |
. . . . 5
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7 | djulf1o 7056 |
. . . . . . . . 9
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8 | f1ocnv 5474 |
. . . . . . . . 9
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9 | f1ofun 5463 |
. . . . . . . . 9
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10 | 7, 8, 9 | mp2b 8 |
. . . . . . . 8
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11 | vex 2740 |
. . . . . . . 8
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12 | cofunexg 6109 |
. . . . . . . 8
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13 | 10, 11, 12 | mp2an 426 |
. . . . . . 7
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14 | foeq1 5434 |
. . . . . . 7
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15 | 13, 14 | spcev 2832 |
. . . . . 6
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16 | 15 | 3anim2i 1186 |
. . . . 5
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17 | 6, 16 | syl 14 |
. . . 4
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18 | omex 4592 |
. . . . . 6
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19 | 18 | rabex 4147 |
. . . . 5
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20 | sseq1 3178 |
. . . . . 6
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21 | foeq2 5435 |
. . . . . . 7
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22 | 21 | exbidv 1825 |
. . . . . 6
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23 | eleq2 2241 |
. . . . . . . 8
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24 | 23 | dcbid 838 |
. . . . . . 7
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25 | 24 | ralbidv 2477 |
. . . . . 6
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26 | 20, 22, 25 | 3anbi123d 1312 |
. . . . 5
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27 | 19, 26 | spcev 2832 |
. . . 4
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28 | 17, 27 | syl 14 |
. . 3
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29 | 28 | exlimiv 1598 |
. 2
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30 | 2, 29 | sylbi 121 |
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-coll 4118 ax-sep 4121 ax-nul 4129 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-iinf 4587 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-3an 980 df-tru 1356 df-fal 1359 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-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-csb 3058 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-int 3845 df-iun 3888 df-br 4004 df-opab 4065 df-mpt 4066 df-tr 4102 df-id 4293 df-iord 4366 df-on 4368 df-suc 4371 df-iom 4590 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-f1 5221 df-fo 5222 df-f1o 5223 df-fv 5224 df-1st 6140 df-2nd 6141 df-1o 6416 df-dju 7036 df-inl 7045 df-inr 7046 |
This theorem is referenced by: ctssdc 7111 |
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