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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 10593 | . . . . . 6 |
3 | 2 | breqd 3940 | . . . . 5 |
4 | vex 2689 | . . . . . 6 | |
5 | eleq1 2202 | . . . . . . . 8 | |
6 | oveq1 5781 | . . . . . . . . 9 | |
7 | 6 | breq1d 3939 | . . . . . . . 8 |
8 | 5, 7 | anbi12d 464 | . . . . . . 7 |
9 | breq2 3933 | . . . . . . . 8 | |
10 | 9 | anbi2d 459 | . . . . . . 7 |
11 | eqid 2139 | . . . . . . 7 | |
12 | 8, 10, 11 | brabg 4191 | . . . . . 6 |
13 | 4, 12 | mpan2 421 | . . . . 5 |
14 | 3, 13 | sylan9bb 457 | . . . 4 |
15 | ibar 299 | . . . . 5 | |
16 | 15 | adantl 275 | . . . 4 |
17 | 14, 16 | bitr4d 190 | . . 3 |
18 | 17 | abbidv 2257 | . 2 |
19 | imasng 4904 | . . 3 | |
20 | 19 | adantl 275 | . 2 |
21 | simpr 109 | . . . 4 | |
22 | simpl 108 | . . . 4 | |
23 | 21, 22 | subcld 8073 | . . 3 |
24 | imasng 4904 | . . 3 | |
25 | 23, 24 | syl 14 | . 2 |
26 | 18, 20, 25 | 3eqtr4d 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cab 2125 cvv 2686 csn 3527 class class class wbr 3929 copab 3988 cima 4542 (class class class)co 5774 cc 7618 cmin 7933 cshi 10586 |
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 603 ax-in2 604 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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-coll 4043 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-resscn 7712 ax-1cn 7713 ax-icn 7715 ax-addcl 7716 ax-addrcl 7717 ax-mulcl 7718 ax-addcom 7720 ax-addass 7722 ax-distr 7724 ax-i2m1 7725 ax-0id 7728 ax-rnegex 7729 ax-cnre 7731 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-riota 5730 df-ov 5777 df-oprab 5778 df-mpo 5779 df-sub 7935 df-shft 10587 |
This theorem is referenced by: shftval 10597 |
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