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Mirrors > Home > ILE Home > Th. List > fvelimab | Unicode version |
Description: Function value in an image. (Contributed by NM, 20-Jan-2007.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) (Revised by David Abernethy, 17-Dec-2011.) |
Ref | Expression |
---|---|
fvelimab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2566 | . . . 4 | |
2 | 1 | anim2i 324 | . . 3 |
3 | ssel2 2940 | . . . . . . . 8 | |
4 | funfvex 5192 | . . . . . . . . 9 | |
5 | 4 | funfni 4999 | . . . . . . . 8 |
6 | 3, 5 | sylan2 270 | . . . . . . 7 |
7 | 6 | anassrs 380 | . . . . . 6 |
8 | eleq1 2100 | . . . . . 6 | |
9 | 7, 8 | syl5ibcom 144 | . . . . 5 |
10 | 9 | rexlimdva 2433 | . . . 4 |
11 | 10 | imdistani 419 | . . 3 |
12 | eleq1 2100 | . . . . . . 7 | |
13 | eqeq2 2049 | . . . . . . . 8 | |
14 | 13 | rexbidv 2327 | . . . . . . 7 |
15 | 12, 14 | bibi12d 224 | . . . . . 6 |
16 | 15 | imbi2d 219 | . . . . 5 |
17 | fnfun 4996 | . . . . . . . 8 | |
18 | 17 | adantr 261 | . . . . . . 7 |
19 | fndm 4998 | . . . . . . . . 9 | |
20 | 19 | sseq2d 2973 | . . . . . . . 8 |
21 | 20 | biimpar 281 | . . . . . . 7 |
22 | dfimafn 5222 | . . . . . . 7 | |
23 | 18, 21, 22 | syl2anc 391 | . . . . . 6 |
24 | 23 | abeq2d 2150 | . . . . 5 |
25 | 16, 24 | vtoclg 2613 | . . . 4 |
26 | 25 | impcom 116 | . . 3 |
27 | 2, 11, 26 | pm5.21nd 825 | . 2 |
28 | fveq2 5178 | . . . 4 | |
29 | 28 | eqeq1d 2048 | . . 3 |
30 | 29 | cbvrexv 2534 | . 2 |
31 | 27, 30 | syl6bb 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 cab 2026 wrex 2307 cvv 2557 wss 2917 cdm 4345 cima 4348 wfun 4896 wfn 4897 cfv 4902 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-fv 4910 |
This theorem is referenced by: ssimaex 5234 rexima 5394 ralima 5395 f1elima 5412 ovelimab 5651 |
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