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Mirrors > Home > ILE Home > Th. List > fsnunfv | Unicode version |
Description: Recover the added point from a point-added function. (Contributed by Stefan O'Rear, 28-Feb-2015.) (Revised by NM, 18-May-2017.) |
Ref | Expression |
---|---|
fsnunfv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmres 4835 | . . . . . . . . 9 | |
2 | incom 3263 | . . . . . . . . 9 | |
3 | 1, 2 | eqtri 2158 | . . . . . . . 8 |
4 | disjsn 3580 | . . . . . . . . 9 | |
5 | 4 | biimpri 132 | . . . . . . . 8 |
6 | 3, 5 | syl5eq 2182 | . . . . . . 7 |
7 | 6 | 3ad2ant3 1004 | . . . . . 6 |
8 | relres 4842 | . . . . . . 7 | |
9 | reldm0 4752 | . . . . . . 7 | |
10 | 8, 9 | ax-mp 5 | . . . . . 6 |
11 | 7, 10 | sylibr 133 | . . . . 5 |
12 | fnsng 5165 | . . . . . . 7 | |
13 | 12 | 3adant3 1001 | . . . . . 6 |
14 | fnresdm 5227 | . . . . . 6 | |
15 | 13, 14 | syl 14 | . . . . 5 |
16 | 11, 15 | uneq12d 3226 | . . . 4 |
17 | resundir 4828 | . . . 4 | |
18 | uncom 3215 | . . . . 5 | |
19 | un0 3391 | . . . . 5 | |
20 | 18, 19 | eqtr2i 2159 | . . . 4 |
21 | 16, 17, 20 | 3eqtr4g 2195 | . . 3 |
22 | 21 | fveq1d 5416 | . 2 |
23 | snidg 3549 | . . . 4 | |
24 | 23 | 3ad2ant1 1002 | . . 3 |
25 | fvres 5438 | . . 3 | |
26 | 24, 25 | syl 14 | . 2 |
27 | fvsng 5609 | . . 3 | |
28 | 27 | 3adant3 1001 | . 2 |
29 | 22, 26, 28 | 3eqtr3d 2178 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 w3a 962 wceq 1331 wcel 1480 cun 3064 cin 3065 c0 3358 csn 3522 cop 3525 cdm 4534 cres 4536 wrel 4539 wfn 5113 cfv 5118 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-res 4546 df-iota 5083 df-fun 5120 df-fn 5121 df-fv 5126 |
This theorem is referenced by: tfrlemisucaccv 6215 tfr1onlemsucaccv 6231 tfrcllemsucaccv 6244 inftonninf 10207 hashinfom 10517 zfz1isolemiso 10575 fvsetsid 11982 |
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