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Mirrors > Home > ILE Home > Th. List > fodjumkvlemres | Unicode version |
Description: Lemma for fodjumkv 7151. The final result with ![]() |
Ref | Expression |
---|---|
fodjumkv.o |
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fodjumkv.fo |
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fodjumkv.p |
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Ref | Expression |
---|---|
fodjumkvlemres |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fodjumkv.fo |
. . . . . 6
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2 | 1 | adantr 276 |
. . . . 5
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3 | fodjumkv.p |
. . . . 5
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4 | simpr 110 |
. . . . 5
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5 | 2, 3, 4 | fodju0 7138 |
. . . 4
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6 | 5 | ex 115 |
. . 3
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7 | 6 | necon3ad 2389 |
. 2
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8 | fveq1 5509 |
. . . . . . 7
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9 | 8 | eqeq1d 2186 |
. . . . . 6
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10 | 9 | ralbidv 2477 |
. . . . 5
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11 | 10 | notbid 667 |
. . . 4
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12 | 8 | eqeq1d 2186 |
. . . . 5
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13 | 12 | rexbidv 2478 |
. . . 4
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14 | 11, 13 | imbi12d 234 |
. . 3
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15 | fodjumkv.o |
. . . 4
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16 | ismkvmap 7145 |
. . . . 5
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17 | 16 | ibi 176 |
. . . 4
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18 | 15, 17 | syl 14 |
. . 3
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19 | 1, 3, 15 | fodjuf 7136 |
. . 3
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20 | 14, 18, 19 | rspcdva 2846 |
. 2
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21 | 1 | adantr 276 |
. . . 4
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22 | simpr 110 |
. . . . 5
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23 | fveqeq2 5519 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23 | cbvrexv 2704 |
. . . . 5
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25 | 22, 24 | sylib 122 |
. . . 4
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26 | 21, 3, 25 | fodjum 7137 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 26 | ex 115 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | 7, 20, 27 | 3syld 57 |
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 4205 ax-un 4429 ax-setind 4532 |
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-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-if 3535 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-int 3843 df-br 4001 df-opab 4062 df-mpt 4063 df-tr 4099 df-id 4289 df-iord 4362 df-on 4364 df-suc 4367 df-iom 4586 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-rn 4633 df-res 4634 df-ima 4635 df-iota 5173 df-fun 5213 df-fn 5214 df-f 5215 df-f1 5216 df-fo 5217 df-f1o 5218 df-fv 5219 df-ov 5871 df-oprab 5872 df-mpo 5873 df-1st 6134 df-2nd 6135 df-1o 6410 df-2o 6411 df-map 6643 df-dju 7030 df-inl 7039 df-inr 7040 df-markov 7143 |
This theorem is referenced by: fodjumkv 7151 |
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