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Mirrors > Home > ILE Home > Th. List > fconstfvm | Unicode version |
Description: A constant function expressed in terms of its functionality, domain, and value. See also fconst2 5514. (Contributed by Jim Kingdon, 8-Jan-2019.) |
Ref | Expression |
---|---|
fconstfvm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5161 |
. . 3
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2 | fvconst 5485 |
. . . 4
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3 | 2 | ralrimiva 2446 |
. . 3
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4 | 1, 3 | jca 300 |
. 2
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5 | fvelrnb 5352 |
. . . . . . . . 9
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6 | fveq2 5305 |
. . . . . . . . . . . . . 14
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7 | 6 | eqeq1d 2096 |
. . . . . . . . . . . . 13
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8 | 7 | rspccva 2721 |
. . . . . . . . . . . 12
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9 | 8 | eqeq1d 2096 |
. . . . . . . . . . 11
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10 | 9 | rexbidva 2377 |
. . . . . . . . . 10
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11 | r19.9rmv 3373 |
. . . . . . . . . . 11
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12 | 11 | bicomd 139 |
. . . . . . . . . 10
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13 | 10, 12 | sylan9bbr 451 |
. . . . . . . . 9
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14 | 5, 13 | sylan9bbr 451 |
. . . . . . . 8
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15 | velsn 3463 |
. . . . . . . . 9
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16 | eqcom 2090 |
. . . . . . . . 9
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17 | 15, 16 | bitr2i 183 |
. . . . . . . 8
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18 | 14, 17 | syl6bb 194 |
. . . . . . 7
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19 | 18 | eqrdv 2086 |
. . . . . 6
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20 | 19 | an32s 535 |
. . . . 5
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21 | 20 | exp31 356 |
. . . 4
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22 | 21 | imdistand 436 |
. . 3
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23 | df-fo 5021 |
. . . 4
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24 | fof 5233 |
. . . 4
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25 | 23, 24 | sylbir 133 |
. . 3
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26 | 22, 25 | syl6 33 |
. 2
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27 | 4, 26 | impbid2 141 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-sbc 2841 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-mpt 3901 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-iota 4980 df-fun 5017 df-fn 5018 df-f 5019 df-fo 5021 df-fv 5023 |
This theorem is referenced by: fconst3m 5516 |
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