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Mirrors > Home > ILE Home > Th. List > fvtp1g | Unicode version |
Description: The value of a function with a domain of (at most) three elements. (Contributed by Alexander van der Vekens, 4-Dec-2017.) |
Ref | Expression |
---|---|
fvtp1g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-tp 3406 | . . 3 | |
2 | 1 | fveq1i 5199 | . 2 |
3 | necom 2329 | . . . . 5 | |
4 | fvunsng 5378 | . . . . 5 | |
5 | 3, 4 | sylan2b 281 | . . . 4 |
6 | 5 | ad2ant2rl 494 | . . 3 |
7 | fvpr1g 5388 | . . . . 5 | |
8 | 7 | 3expa 1138 | . . . 4 |
9 | 8 | adantrr 462 | . . 3 |
10 | 6, 9 | eqtrd 2113 | . 2 |
11 | 2, 10 | syl5eq 2125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 wne 2245 cun 2971 csn 3398 cpr 3399 ctp 3400 cop 3401 cfv 4922 |
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-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-tp 3406 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-res 4375 df-iota 4887 df-fun 4924 df-fv 4930 |
This theorem is referenced by: fvtp2g 5391 fvtp1 5393 |
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