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Mirrors > Home > MPE Home > Th. List > isores2 | Structured version Visualization version 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 5812 |
. . . . . . . 8
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2 | ffvelrn 6018 |
. . . . . . . . . 10
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3 | 2 | adantrr 722 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | ffvelrn 6018 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | adantrl 721 |
. . . . . . . . 9
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6 | brinxp 4896 |
. . . . . . . . 9
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7 | 3, 5, 6 | syl2anc 666 |
. . . . . . . 8
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8 | 1, 7 | sylan 474 |
. . . . . . 7
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9 | 8 | anassrs 653 |
. . . . . 6
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10 | 9 | bibi2d 320 |
. . . . 5
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11 | 10 | ralbidva 2823 |
. . . 4
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12 | 11 | ralbidva 2823 |
. . 3
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13 | 12 | pm5.32i 642 |
. 2
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14 | df-isom 5590 |
. 2
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15 | df-isom 5590 |
. 2
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16 | 13, 14, 15 | 3bitr4i 281 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pr 4638 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-f1 5586 df-f1o 5588 df-fv 5589 df-isom 5590 |
This theorem is referenced by: isores1 6223 hartogslem1 8054 leiso 12619 icopnfhmeo 21964 iccpnfhmeo 21966 gtiso 28274 xrge0iifhmeo 28735 |
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