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Mirrors > Home > ILE Home > Th. List > mapsnf1o3 | Unicode version |
Description: Explicit bijection in the reverse of mapsnf1o2 6643. (Contributed by Stefan O'Rear, 24-Mar-2015.) |
Ref | Expression |
---|---|
mapsncnv.s | |
mapsncnv.b | |
mapsncnv.x | |
mapsnf1o3.f |
Ref | Expression |
---|---|
mapsnf1o3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mapsncnv.s | . . . 4 | |
2 | mapsncnv.b | . . . 4 | |
3 | mapsncnv.x | . . . 4 | |
4 | eqid 2157 | . . . 4 | |
5 | 1, 2, 3, 4 | mapsnf1o2 6643 | . . 3 |
6 | f1ocnv 5429 | . . 3 | |
7 | 5, 6 | ax-mp 5 | . 2 |
8 | mapsnf1o3.f | . . . 4 | |
9 | 1, 2, 3, 4 | mapsncnv 6642 | . . . 4 |
10 | 8, 9 | eqtr4i 2181 | . . 3 |
11 | f1oeq1 5405 | . . 3 | |
12 | 10, 11 | ax-mp 5 | . 2 |
13 | 7, 12 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 wcel 2128 cvv 2712 csn 3561 cmpt 4027 cxp 4586 ccnv 4587 wf1o 5171 cfv 5172 (class class class)co 5826 cmap 6595 |
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-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 ax-setind 4498 |
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-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-ima 4601 df-iota 5137 df-fun 5174 df-fn 5175 df-f 5176 df-f1 5177 df-fo 5178 df-f1o 5179 df-fv 5180 df-ov 5829 df-oprab 5830 df-mpo 5831 df-map 6597 |
This theorem is referenced by: (None) |
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