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Mirrors > Home > ILE Home > Th. List > isores2 | Unicode version |
Description: An isomorphism from one well-order to another can be restricted on either well-order. (Contributed by Mario Carneiro, 15-Jan-2013.) |
Ref | Expression |
---|---|
isores2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1of 5413 | . . . . . . . 8 | |
2 | ffvelrn 5599 | . . . . . . . . . 10 | |
3 | 2 | adantrr 471 | . . . . . . . . 9 |
4 | ffvelrn 5599 | . . . . . . . . . 10 | |
5 | 4 | adantrl 470 | . . . . . . . . 9 |
6 | brinxp 4653 | . . . . . . . . 9 | |
7 | 3, 5, 6 | syl2anc 409 | . . . . . . . 8 |
8 | 1, 7 | sylan 281 | . . . . . . 7 |
9 | 8 | anassrs 398 | . . . . . 6 |
10 | 9 | bibi2d 231 | . . . . 5 |
11 | 10 | ralbidva 2453 | . . . 4 |
12 | 11 | ralbidva 2453 | . . 3 |
13 | 12 | pm5.32i 450 | . 2 |
14 | df-isom 5178 | . 2 | |
15 | df-isom 5178 | . 2 | |
16 | 13, 14, 15 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wcel 2128 wral 2435 cin 3101 class class class wbr 3965 cxp 4583 wf 5165 wf1o 5168 cfv 5169 wiso 5170 |
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-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-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 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-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 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-br 3966 df-opab 4026 df-id 4253 df-xp 4591 df-rel 4592 df-cnv 4593 df-co 4594 df-dm 4595 df-rn 4596 df-iota 5134 df-fun 5171 df-fn 5172 df-f 5173 df-f1 5174 df-f1o 5176 df-fv 5177 df-isom 5178 |
This theorem is referenced by: isores1 5761 |
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