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Mirrors > Home > ILE Home > Th. List > fvopab3ig | Unicode version |
Description: Value of a function given by ordered-pair class abstraction. (Contributed by NM, 23-Oct-1999.) |
Ref | Expression |
---|---|
fvopab3ig.1 |
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fvopab3ig.2 |
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fvopab3ig.3 |
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fvopab3ig.4 |
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Ref | Expression |
---|---|
fvopab3ig |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2252 |
. . . . . . . 8
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2 | fvopab3ig.1 |
. . . . . . . 8
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3 | 1, 2 | anbi12d 473 |
. . . . . . 7
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4 | fvopab3ig.2 |
. . . . . . . 8
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5 | 4 | anbi2d 464 |
. . . . . . 7
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6 | 3, 5 | opelopabg 4286 |
. . . . . 6
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7 | 6 | biimpar 297 |
. . . . 5
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8 | 7 | exp43 372 |
. . . 4
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9 | 8 | pm2.43a 51 |
. . 3
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10 | 9 | imp 124 |
. 2
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11 | fvopab3ig.4 |
. . . 4
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12 | 11 | fveq1i 5535 |
. . 3
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13 | funopab 5270 |
. . . . 5
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14 | fvopab3ig.3 |
. . . . . 6
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15 | moanimv 2113 |
. . . . . 6
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16 | 14, 15 | mpbir 146 |
. . . . 5
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17 | 13, 16 | mpgbir 1464 |
. . . 4
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18 | funopfv 5576 |
. . . 4
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19 | 17, 18 | ax-mp 5 |
. . 3
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20 | 12, 19 | eqtrid 2234 |
. 2
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21 | 10, 20 | syl6 33 |
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-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-v 2754 df-sbc 2978 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-br 4019 df-opab 4080 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-iota 5196 df-fun 5237 df-fv 5243 |
This theorem is referenced by: fvmptg 5613 fvopab6 5633 ov6g 6034 |
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