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Mirrors > Home > MPE Home > Th. List > hashinf | Structured version Visualization version Unicode version |
Description: The value of the ![]() |
Ref | Expression |
---|---|
hashinf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3040 |
. 2
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2 | eldif 3400 |
. . 3
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3 | df-hash 12554 |
. . . . . . 7
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4 | 3 | reseq1i 5107 |
. . . . . 6
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5 | resundir 5125 |
. . . . . 6
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6 | disjdif 3830 |
. . . . . . . . 9
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7 | eqid 2471 |
. . . . . . . . . . 11
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8 | eqid 2471 |
. . . . . . . . . . 11
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9 | 7, 8 | hashkf 12555 |
. . . . . . . . . 10
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10 | ffn 5739 |
. . . . . . . . . 10
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11 | fnresdisj 5696 |
. . . . . . . . . 10
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12 | 9, 10, 11 | mp2b 10 |
. . . . . . . . 9
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13 | 6, 12 | mpbi 213 |
. . . . . . . 8
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14 | pnfex 11436 |
. . . . . . . . . 10
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15 | 14 | fconst 5782 |
. . . . . . . . 9
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16 | ffn 5739 |
. . . . . . . . 9
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17 | fnresdm 5695 |
. . . . . . . . 9
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18 | 15, 16, 17 | mp2b 10 |
. . . . . . . 8
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19 | 13, 18 | uneq12i 3577 |
. . . . . . 7
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20 | uncom 3569 |
. . . . . . 7
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21 | un0 3762 |
. . . . . . 7
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22 | 19, 20, 21 | 3eqtri 2497 |
. . . . . 6
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23 | 4, 5, 22 | 3eqtri 2497 |
. . . . 5
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24 | 23 | fveq1i 5880 |
. . . 4
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25 | fvres 5893 |
. . . 4
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26 | 14 | fvconst2 6136 |
. . . 4
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27 | 24, 25, 26 | 3eqtr3a 2529 |
. . 3
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28 | 2, 27 | sylbir 218 |
. 2
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29 | 1, 28 | sylan 479 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602 ax-cnex 9613 ax-resscn 9614 ax-1cn 9615 ax-icn 9616 ax-addcl 9617 ax-addrcl 9618 ax-mulcl 9619 ax-mulrcl 9620 ax-mulcom 9621 ax-addass 9622 ax-mulass 9623 ax-distr 9624 ax-i2m1 9625 ax-1ne0 9626 ax-1rid 9627 ax-rnegex 9628 ax-rrecex 9629 ax-cnre 9630 ax-pre-lttri 9631 ax-pre-lttrn 9632 ax-pre-ltadd 9633 ax-pre-mulgt0 9634 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-nel 2644 df-ral 2761 df-rex 2762 df-reu 2763 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-pss 3406 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-tp 3964 df-op 3966 df-uni 4191 df-int 4227 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-tr 4491 df-eprel 4750 df-id 4754 df-po 4760 df-so 4761 df-fr 4798 df-we 4800 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-pred 5387 df-ord 5433 df-on 5434 df-lim 5435 df-suc 5436 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-riota 6270 df-ov 6311 df-oprab 6312 df-mpt2 6313 df-om 6712 df-wrecs 7046 df-recs 7108 df-rdg 7146 df-er 7381 df-en 7588 df-dom 7589 df-sdom 7590 df-fin 7591 df-card 8391 df-pnf 9695 df-mnf 9696 df-xr 9697 df-ltxr 9698 df-le 9699 df-sub 9882 df-neg 9883 df-nn 10632 df-n0 10894 df-z 10962 df-uz 11183 df-hash 12554 |
This theorem is referenced by: hashbnd 12559 hasheni 12569 hasheqf1oi 12572 hashclb 12578 hasheq0 12582 hashdom 12596 hashdomi 12597 hashunx 12603 hashge1 12606 hashss 12624 hash1snb 12634 hashge2el2dif 12678 odhash 17301 lt6abl 17607 umgrafi 25128 sizeusglecusg 25293 hashnbgravdg 25720 esumpinfsum 28972 hasheuni 28980 nfile 39217 upgrfi 39337 pgrpgt2nabl 40659 |
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