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Mirrors > Home > ILE Home > Th. List > fv3 | Unicode version |
Description: Alternate definition of the value of a function. Definition 6.11 of [TakeutiZaring] p. 26. (Contributed by NM, 30-Apr-2004.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fv3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfv 5176 | . . 3 | |
2 | bi2 121 | . . . . . . . . . 10 | |
3 | 2 | alimi 1344 | . . . . . . . . 9 |
4 | vex 2560 | . . . . . . . . . 10 | |
5 | breq2 3768 | . . . . . . . . . 10 | |
6 | 4, 5 | ceqsalv 2584 | . . . . . . . . 9 |
7 | 3, 6 | sylib 127 | . . . . . . . 8 |
8 | 7 | anim2i 324 | . . . . . . 7 |
9 | 8 | eximi 1491 | . . . . . 6 |
10 | elequ2 1601 | . . . . . . . 8 | |
11 | breq2 3768 | . . . . . . . 8 | |
12 | 10, 11 | anbi12d 442 | . . . . . . 7 |
13 | 12 | cbvexv 1795 | . . . . . 6 |
14 | 9, 13 | sylib 127 | . . . . 5 |
15 | exsimpr 1509 | . . . . . 6 | |
16 | df-eu 1903 | . . . . . 6 | |
17 | 15, 16 | sylibr 137 | . . . . 5 |
18 | 14, 17 | jca 290 | . . . 4 |
19 | nfeu1 1911 | . . . . . . 7 | |
20 | nfv 1421 | . . . . . . . . 9 | |
21 | nfa1 1434 | . . . . . . . . 9 | |
22 | 20, 21 | nfan 1457 | . . . . . . . 8 |
23 | 22 | nfex 1528 | . . . . . . 7 |
24 | 19, 23 | nfim 1464 | . . . . . 6 |
25 | bi1 111 | . . . . . . . . . . . . . 14 | |
26 | ax-14 1405 | . . . . . . . . . . . . . 14 | |
27 | 25, 26 | syl6 29 | . . . . . . . . . . . . 13 |
28 | 27 | com23 72 | . . . . . . . . . . . 12 |
29 | 28 | impd 242 | . . . . . . . . . . 11 |
30 | 29 | sps 1430 | . . . . . . . . . 10 |
31 | 30 | anc2ri 313 | . . . . . . . . 9 |
32 | 31 | com12 27 | . . . . . . . 8 |
33 | 32 | eximdv 1760 | . . . . . . 7 |
34 | 16, 33 | syl5bi 141 | . . . . . 6 |
35 | 24, 34 | exlimi 1485 | . . . . 5 |
36 | 35 | imp 115 | . . . 4 |
37 | 18, 36 | impbii 117 | . . 3 |
38 | 1, 37 | bitri 173 | . 2 |
39 | 38 | abbi2i 2152 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 weu 1900 cab 2026 class class class wbr 3764 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 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 |
This theorem is referenced by: (None) |
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