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Mirrors > Home > ILE Home > Th. List > fpr | Unicode version |
Description: A function with a domain of two elements. (Contributed by Jeff Madsen, 20-Jun-2010.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
fpr.1 |
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fpr.2 |
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fpr.3 |
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fpr.4 |
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Ref | Expression |
---|---|
fpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fpr.1 |
. . . . . 6
![]() ![]() ![]() ![]() | |
2 | fpr.2 |
. . . . . 6
![]() ![]() ![]() ![]() | |
3 | fpr.3 |
. . . . . 6
![]() ![]() ![]() ![]() | |
4 | fpr.4 |
. . . . . 6
![]() ![]() ![]() ![]() | |
5 | 1, 2, 3, 4 | funpr 5287 |
. . . . 5
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6 | 3, 4 | dmprop 5121 |
. . . . 5
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7 | 5, 6 | jctir 313 |
. . . 4
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8 | df-fn 5238 |
. . . 4
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9 | 7, 8 | sylibr 134 |
. . 3
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10 | df-pr 3614 |
. . . . . 6
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11 | 10 | rneqi 4873 |
. . . . 5
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12 | rnun 5055 |
. . . . 5
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13 | 1 | rnsnop 5127 |
. . . . . . 7
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14 | 2 | rnsnop 5127 |
. . . . . . 7
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15 | 13, 14 | uneq12i 3302 |
. . . . . 6
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16 | df-pr 3614 |
. . . . . 6
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17 | 15, 16 | eqtr4i 2213 |
. . . . 5
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18 | 11, 12, 17 | 3eqtri 2214 |
. . . 4
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19 | 18 | eqimssi 3226 |
. . 3
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20 | 9, 19 | jctir 313 |
. 2
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21 | df-f 5239 |
. 2
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22 | 20, 21 | sylibr 134 |
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 615 ax-in2 616 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-fal 1370 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-ne 2361 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 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-rn 4655 df-fun 5237 df-fn 5238 df-f 5239 |
This theorem is referenced by: (None) |
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