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Mirrors > Home > MPE Home > Th. List > isso2i | Structured version Visualization version Unicode version |
Description: Deduce strict ordering from its properties. (Contributed by NM, 29-Jan-1996.) (Revised by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
isso2i.1 |
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isso2i.2 |
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Ref | Expression |
---|---|
isso2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1854 |
. . . . 5
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2 | 1 | orci 392 |
. . . 4
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3 | eleq1 2516 |
. . . . . . 7
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4 | 3 | anbi2d 709 |
. . . . . 6
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5 | equequ2 1867 |
. . . . . . . 8
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6 | breq1 4404 |
. . . . . . . 8
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7 | 5, 6 | orbi12d 715 |
. . . . . . 7
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8 | breq2 4405 |
. . . . . . . 8
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9 | 8 | notbid 296 |
. . . . . . 7
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10 | 7, 9 | bibi12d 323 |
. . . . . 6
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11 | 4, 10 | imbi12d 322 |
. . . . 5
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12 | isso2i.1 |
. . . . . 6
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13 | 12 | con2bid 331 |
. . . . 5
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14 | 11, 13 | chvarv 2106 |
. . . 4
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15 | 2, 14 | mpbii 215 |
. . 3
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16 | 15 | anidms 650 |
. 2
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17 | isso2i.2 |
. 2
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18 | 13 | biimprd 227 |
. . 3
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19 | 3orass 987 |
. . . 4
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20 | df-or 372 |
. . . 4
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21 | 19, 20 | bitri 253 |
. . 3
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22 | 18, 21 | sylibr 216 |
. 2
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23 | 16, 17, 22 | issoi 4785 |
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-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 985 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ral 2741 df-rab 2745 df-v 3046 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-br 4402 df-po 4754 df-so 4755 |
This theorem is referenced by: ltsonq 9391 ltsosr 9515 ltso 9711 xrltso 11437 |
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