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Mirrors > Home > ILE Home > Th. List > ofrval | Unicode version |
Description: Exhibit a function relation at a point. (Contributed by Mario Carneiro, 28-Jul-2014.) |
Ref | Expression |
---|---|
offval.1 |
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offval.2 |
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offval.3 |
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offval.4 |
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offval.5 |
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ofrval.6 |
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ofrval.7 |
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Ref | Expression |
---|---|
ofrval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | offval.1 |
. . . . . 6
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2 | offval.2 |
. . . . . 6
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3 | offval.3 |
. . . . . 6
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4 | offval.4 |
. . . . . 6
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5 | offval.5 |
. . . . . 6
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6 | eqidd 2190 |
. . . . . 6
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7 | eqidd 2190 |
. . . . . 6
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8 | 1, 2, 3, 4, 5, 6, 7 | ofrfval 6116 |
. . . . 5
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9 | 8 | biimpa 296 |
. . . 4
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10 | fveq2 5534 |
. . . . . 6
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11 | fveq2 5534 |
. . . . . 6
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12 | 10, 11 | breq12d 4031 |
. . . . 5
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13 | 12 | rspccv 2853 |
. . . 4
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14 | 9, 13 | syl 14 |
. . 3
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15 | 14 | 3impia 1202 |
. 2
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16 | simp1 999 |
. . 3
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17 | inss1 3370 |
. . . . 5
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18 | 5, 17 | eqsstrri 3203 |
. . . 4
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19 | simp3 1001 |
. . . 4
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20 | 18, 19 | sselid 3168 |
. . 3
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21 | ofrval.6 |
. . 3
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22 | 16, 20, 21 | syl2anc 411 |
. 2
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23 | inss2 3371 |
. . . . 5
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24 | 5, 23 | eqsstrri 3203 |
. . . 4
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25 | 24, 19 | sselid 3168 |
. . 3
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26 | ofrval.7 |
. . 3
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27 | 16, 25, 26 | syl2anc 411 |
. 2
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28 | 15, 22, 27 | 3brtr3d 4049 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-coll 4133 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 df-fv 5243 df-ofr 6108 |
This theorem is referenced by: psrbaglesuppg 13967 |
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