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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 5828 |
. . . . . . . 8
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2 | ffvelrn 6035 |
. . . . . . . . . 10
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3 | 2 | adantrr 731 |
. . . . . . . . 9
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4 | ffvelrn 6035 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | adantrl 730 |
. . . . . . . . 9
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6 | brinxp 4902 |
. . . . . . . . 9
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7 | 3, 5, 6 | syl2anc 673 |
. . . . . . . 8
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8 | 1, 7 | sylan 479 |
. . . . . . 7
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9 | 8 | anassrs 660 |
. . . . . 6
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10 | 9 | bibi2d 325 |
. . . . 5
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11 | 10 | ralbidva 2828 |
. . . 4
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12 | 11 | ralbidva 2828 |
. . 3
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13 | 12 | pm5.32i 649 |
. 2
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14 | df-isom 5598 |
. 2
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15 | df-isom 5598 |
. 2
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16 | 13, 14, 15 | 3bitr4i 285 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-id 4754 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-f1o 5596 df-fv 5597 df-isom 5598 |
This theorem is referenced by: isores1 6243 hartogslem1 8075 leiso 12663 icopnfhmeo 22049 iccpnfhmeo 22051 gtiso 28356 xrge0iifhmeo 28816 |
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