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Mirrors > Home > MPE Home > Th. List > fvopab3ig | Structured version 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 2523 |
. . . . . . . 8
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2 | fvopab3ig.1 |
. . . . . . . 8
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3 | 1, 2 | anbi12d 710 |
. . . . . . 7
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4 | fvopab3ig.2 |
. . . . . . . 8
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5 | 4 | anbi2d 703 |
. . . . . . 7
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6 | 3, 5 | opelopabg 4708 |
. . . . . 6
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7 | 6 | biimpar 485 |
. . . . 5
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8 | 7 | exp43 612 |
. . . 4
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9 | 8 | pm2.43a 49 |
. . 3
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10 | 9 | imp 429 |
. 2
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11 | fvopab3ig.4 |
. . . 4
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12 | 11 | fveq1i 5793 |
. . 3
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13 | funopab 5552 |
. . . . 5
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14 | fvopab3ig.3 |
. . . . . 6
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15 | moanimv 2341 |
. . . . . 6
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16 | 14, 15 | mpbir 209 |
. . . . 5
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17 | 13, 16 | mpgbir 1596 |
. . . 4
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18 | funopfv 5833 |
. . . 4
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19 | 17, 18 | ax-mp 5 |
. . 3
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20 | 12, 19 | syl5eq 2504 |
. 2
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21 | 10, 20 | syl6 33 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4514 ax-nul 4522 ax-pr 4632 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3073 df-sbc 3288 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-op 3985 df-uni 4193 df-br 4394 df-opab 4452 df-id 4737 df-xp 4947 df-rel 4948 df-cnv 4949 df-co 4950 df-dm 4951 df-iota 5482 df-fun 5521 df-fv 5527 |
This theorem is referenced by: fvmptg 5874 fvopab6 5898 ov6g 6331 |
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