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Mirrors > Home > ILE Home > Th. List > fodjuomnilemdc | Unicode version |
Description: Lemma for fodjuomni 7141. Decidability of a condition we use in various lemmas. (Contributed by Jim Kingdon, 27-Jul-2022.) |
Ref | Expression |
---|---|
fodjuomnilemdc.fo |
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Ref | Expression |
---|---|
fodjuomnilemdc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fodjuomnilemdc.fo |
. . . . . 6
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2 | fof 5434 |
. . . . . 6
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3 | 1, 2 | syl 14 |
. . . . 5
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4 | 3 | ffvelcdmda 5647 |
. . . 4
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5 | djur 7062 |
. . . 4
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6 | 4, 5 | sylib 122 |
. . 3
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7 | nfv 1528 |
. . . . . . . 8
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8 | nfre1 2520 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | nfan 1565 |
. . . . . . 7
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10 | simpr 110 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | fveq2 5511 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 11 | eqeq2d 2189 |
. . . . . . . . . . 11
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13 | 12 | cbvrexv 2704 |
. . . . . . . . . 10
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14 | 10, 13 | sylib 122 |
. . . . . . . . 9
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15 | vex 2740 |
. . . . . . . . . . . . . . 15
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16 | vex 2740 |
. . . . . . . . . . . . . . 15
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17 | djune 7071 |
. . . . . . . . . . . . . . 15
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 15, 16, 17 | mp2an 426 |
. . . . . . . . . . . . . 14
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19 | neeq2 2361 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 18, 19 | mpbiri 168 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 20 | necomd 2433 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | neneqd 2368 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 22 | a1i 9 |
. . . . . . . . . 10
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24 | 23 | rexlimdvw 2598 |
. . . . . . . . 9
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25 | 14, 24 | mpd 13 |
. . . . . . . 8
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26 | 25 | a1d 22 |
. . . . . . 7
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27 | 9, 26 | ralrimi 2548 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | ralnex 2465 |
. . . . . 6
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29 | 27, 28 | sylib 122 |
. . . . 5
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30 | 29 | ex 115 |
. . . 4
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31 | 30 | orim2d 788 |
. . 3
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32 | 6, 31 | mpd 13 |
. 2
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33 | df-dc 835 |
. 2
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34 | 32, 33 | sylibr 134 |
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-sep 4118 ax-nul 4126 ax-pow 4171 ax-pr 4206 ax-un 4430 |
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-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 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-tr 4099 df-id 4290 df-iord 4363 df-on 4365 df-suc 4368 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-rn 4634 df-res 4635 df-iota 5174 df-fun 5214 df-fn 5215 df-f 5216 df-f1 5217 df-fo 5218 df-f1o 5219 df-fv 5220 df-1st 6135 df-2nd 6136 df-1o 6411 df-dju 7031 df-inl 7040 df-inr 7041 |
This theorem is referenced by: fodjuf 7137 fodjum 7138 fodju0 7139 |
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