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Mirrors > Home > ILE Home > Th. List > dffun2 | Unicode version |
Description: Alternate definition of a function. (Contributed by NM, 29-Dec-1996.) |
Ref | Expression |
---|---|
dffun2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fun 5051 |
. 2
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2 | df-id 4144 |
. . . . . 6
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3 | 2 | sseq2i 3066 |
. . . . 5
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4 | df-co 4476 |
. . . . . 6
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5 | 4 | sseq1i 3065 |
. . . . 5
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6 | ssopab2b 4127 |
. . . . 5
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7 | 3, 5, 6 | 3bitri 205 |
. . . 4
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8 | vex 2636 |
. . . . . . . . . . . 12
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9 | vex 2636 |
. . . . . . . . . . . 12
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10 | 8, 9 | brcnv 4650 |
. . . . . . . . . . 11
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11 | 10 | anbi1i 447 |
. . . . . . . . . 10
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12 | 11 | exbii 1548 |
. . . . . . . . 9
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13 | 12 | imbi1i 237 |
. . . . . . . 8
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14 | 19.23v 1818 |
. . . . . . . 8
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15 | 13, 14 | bitr4i 186 |
. . . . . . 7
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16 | 15 | albii 1411 |
. . . . . 6
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17 | alcom 1419 |
. . . . . 6
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18 | 16, 17 | bitri 183 |
. . . . 5
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19 | 18 | albii 1411 |
. . . 4
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20 | alcom 1419 |
. . . 4
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21 | 7, 19, 20 | 3bitri 205 |
. . 3
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22 | 21 | anbi2i 446 |
. 2
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23 | 1, 22 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-v 2635 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-br 3868 df-opab 3922 df-id 4144 df-cnv 4475 df-co 4476 df-fun 5051 |
This theorem is referenced by: dffun4 5060 dffun6f 5062 sbcfung 5073 funcnveq 5111 fliftfun 5613 fclim 10853 |
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