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Mirrors > Home > MPE Home > Th. List > dffv3 | Unicode version |
Description: A definition of function value in terms of iota. (Contributed by Scott Fenton, 19-Feb-2013.) |
Ref | Expression |
---|---|
dffv3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3112 | . . . . 5 | |
2 | elimasng 5368 | . . . . . 6 | |
3 | df-br 4453 | . . . . . 6 | |
4 | 2, 3 | syl6bbr 263 | . . . . 5 |
5 | 1, 4 | mpan2 671 | . . . 4 |
6 | 5 | iotabidv 5577 | . . 3 |
7 | df-fv 5601 | . . 3 | |
8 | 6, 7 | syl6reqr 2517 | . 2 |
9 | fvprc 5865 | . . 3 | |
10 | snprc 4093 | . . . . . . . . 9 | |
11 | 10 | biimpi 194 | . . . . . . . 8 |
12 | 11 | imaeq2d 5342 | . . . . . . 7 |
13 | ima0 5357 | . . . . . . 7 | |
14 | 12, 13 | syl6eq 2514 | . . . . . 6 |
15 | 14 | eleq2d 2527 | . . . . 5 |
16 | 15 | iotabidv 5577 | . . . 4 |
17 | noel 3788 | . . . . . . 7 | |
18 | 17 | nex 1627 | . . . . . 6 |
19 | euex 2308 | . . . . . 6 | |
20 | 18, 19 | mto 176 | . . . . 5 |
21 | iotanul 5571 | . . . . 5 | |
22 | 20, 21 | ax-mp 5 | . . . 4 |
23 | 16, 22 | syl6eq 2514 | . . 3 |
24 | 9, 23 | eqtr4d 2501 | . 2 |
25 | 8, 24 | pm2.61i 164 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -. wn 3 <-> wb 184
/\ wa 369 = wceq 1395 E. wex 1612
e. wcel 1818 E! weu 2282 cvv 3109
c0 3784 { csn 4029 <. cop 4035
class class class wbr 4452 " cima 5007
iota cio 5554 ` cfv 5593 |
This theorem is referenced by: dffv4 5868 fvco2 5948 shftval 12907 dffv5 29574 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-8 1820 ax-9 1822 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 ax-sep 4573 ax-nul 4581 ax-pow 4630 ax-pr 4691 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 975 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-eu 2286 df-mo 2287 df-clab 2443 df-cleq 2449 df-clel 2452 df-nfc 2607 df-ne 2654 df-ral 2812 df-rex 2813 df-rab 2816 df-v 3111 df-sbc 3328 df-dif 3478 df-un 3480 df-in 3482 df-ss 3489 df-nul 3785 df-if 3942 df-sn 4030 df-pr 4032 df-op 4036 df-uni 4250 df-br 4453 df-opab 4511 df-xp 5010 df-cnv 5012 df-dm 5014 df-rn 5015 df-res 5016 df-ima 5017 df-iota 5556 df-fv 5601 |
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