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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 2692 | . . . 4 | |
2 | 1 | anim2i 339 | . . 3 |
3 | ssel2 3087 | . . . . . . . 8 | |
4 | funfvex 5431 | . . . . . . . . 9 | |
5 | 4 | funfni 5218 | . . . . . . . 8 |
6 | 3, 5 | sylan2 284 | . . . . . . 7 |
7 | 6 | anassrs 397 | . . . . . 6 |
8 | eleq1 2200 | . . . . . 6 | |
9 | 7, 8 | syl5ibcom 154 | . . . . 5 |
10 | 9 | rexlimdva 2547 | . . . 4 |
11 | 10 | imdistani 441 | . . 3 |
12 | eleq1 2200 | . . . . . . 7 | |
13 | eqeq2 2147 | . . . . . . . 8 | |
14 | 13 | rexbidv 2436 | . . . . . . 7 |
15 | 12, 14 | bibi12d 234 | . . . . . 6 |
16 | 15 | imbi2d 229 | . . . . 5 |
17 | fnfun 5215 | . . . . . . . 8 | |
18 | 17 | adantr 274 | . . . . . . 7 |
19 | fndm 5217 | . . . . . . . . 9 | |
20 | 19 | sseq2d 3122 | . . . . . . . 8 |
21 | 20 | biimpar 295 | . . . . . . 7 |
22 | dfimafn 5463 | . . . . . . 7 | |
23 | 18, 21, 22 | syl2anc 408 | . . . . . 6 |
24 | 23 | abeq2d 2250 | . . . . 5 |
25 | 16, 24 | vtoclg 2741 | . . . 4 |
26 | 25 | impcom 124 | . . 3 |
27 | 2, 11, 26 | pm5.21nd 901 | . 2 |
28 | fveq2 5414 | . . . 4 | |
29 | 28 | eqeq1d 2146 | . . 3 |
30 | 29 | cbvrexv 2653 | . 2 |
31 | 27, 30 | syl6bb 195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cab 2123 wrex 2415 cvv 2681 wss 3066 cdm 4534 cima 4537 wfun 5112 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-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-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-un 3070 df-in 3072 df-ss 3079 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-rn 4545 df-res 4546 df-ima 4547 df-iota 5083 df-fun 5120 df-fn 5121 df-fv 5126 |
This theorem is referenced by: ssimaex 5475 foima2 5646 rexima 5649 ralima 5650 f1elima 5667 ovelimab 5914 |
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