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Mirrors > Home > ILE Home > Th. List > shftfib | Unicode version |
Description: Value of a fiber of the relation . (Contributed by Mario Carneiro, 4-Nov-2013.) |
Ref | Expression |
---|---|
shftfval.1 |
Ref | Expression |
---|---|
shftfib |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | shftfval.1 | . . . . . . 7 | |
2 | 1 | shftfval 10721 | . . . . . 6 |
3 | 2 | breqd 3976 | . . . . 5 |
4 | vex 2715 | . . . . . 6 | |
5 | eleq1 2220 | . . . . . . . 8 | |
6 | oveq1 5831 | . . . . . . . . 9 | |
7 | 6 | breq1d 3975 | . . . . . . . 8 |
8 | 5, 7 | anbi12d 465 | . . . . . . 7 |
9 | breq2 3969 | . . . . . . . 8 | |
10 | 9 | anbi2d 460 | . . . . . . 7 |
11 | eqid 2157 | . . . . . . 7 | |
12 | 8, 10, 11 | brabg 4229 | . . . . . 6 |
13 | 4, 12 | mpan2 422 | . . . . 5 |
14 | 3, 13 | sylan9bb 458 | . . . 4 |
15 | ibar 299 | . . . . 5 | |
16 | 15 | adantl 275 | . . . 4 |
17 | 14, 16 | bitr4d 190 | . . 3 |
18 | 17 | abbidv 2275 | . 2 |
19 | imasng 4951 | . . 3 | |
20 | 19 | adantl 275 | . 2 |
21 | simpr 109 | . . . 4 | |
22 | simpl 108 | . . . 4 | |
23 | 21, 22 | subcld 8186 | . . 3 |
24 | imasng 4951 | . . 3 | |
25 | 23, 24 | syl 14 | . 2 |
26 | 18, 20, 25 | 3eqtr4d 2200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 cab 2143 cvv 2712 csn 3560 class class class wbr 3965 copab 4024 cima 4589 (class class class)co 5824 cc 7730 cmin 8046 cshi 10714 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-coll 4079 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4496 ax-resscn 7824 ax-1cn 7825 ax-icn 7827 ax-addcl 7828 ax-addrcl 7829 ax-mulcl 7830 ax-addcom 7832 ax-addass 7834 ax-distr 7836 ax-i2m1 7837 ax-0id 7840 ax-rnegex 7841 ax-cnre 7843 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-iun 3851 df-br 3966 df-opab 4026 df-mpt 4027 df-id 4253 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-iota 5135 df-fun 5172 df-fn 5173 df-f 5174 df-f1 5175 df-fo 5176 df-f1o 5177 df-fv 5178 df-riota 5780 df-ov 5827 df-oprab 5828 df-mpo 5829 df-sub 8048 df-shft 10715 |
This theorem is referenced by: shftval 10725 |
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