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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1of 5460 |
. . . . . . . 8
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2 | ffvelcdm 5648 |
. . . . . . . . . 10
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3 | 2 | adantrr 479 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | ffvelcdm 5648 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | adantrl 478 |
. . . . . . . . 9
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6 | brinxp 4693 |
. . . . . . . . 9
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7 | 3, 5, 6 | syl2anc 411 |
. . . . . . . 8
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8 | 1, 7 | sylan 283 |
. . . . . . 7
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9 | 8 | anassrs 400 |
. . . . . 6
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10 | 9 | bibi2d 232 |
. . . . 5
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11 | 10 | ralbidva 2473 |
. . . 4
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12 | 11 | ralbidva 2473 |
. . 3
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13 | 12 | pm5.32i 454 |
. 2
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14 | df-isom 5224 |
. 2
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15 | df-isom 5224 |
. 2
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16 | 13, 14, 15 | 3bitr4i 212 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-iota 5177 df-fun 5217 df-fn 5218 df-f 5219 df-f1 5220 df-f1o 5222 df-fv 5223 df-isom 5224 |
This theorem is referenced by: isores1 5812 |
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