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Mirrors > Home > ILE Home > Th. List > leisorel | Unicode version |
Description: Version of isorel 5717 for strictly increasing functions on the reals. (Contributed by Mario Carneiro, 6-Apr-2015.) (Revised by Mario Carneiro, 9-Sep-2015.) |
Ref | Expression |
---|---|
leisorel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 982 |
. . 3
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2 | simp3r 1011 |
. . 3
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3 | simp3l 1010 |
. . 3
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4 | isorel 5717 |
. . . 4
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5 | 4 | notbid 657 |
. . 3
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6 | 1, 2, 3, 5 | syl12anc 1215 |
. 2
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7 | simp2l 1008 |
. . . 4
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8 | 7, 3 | sseldd 3103 |
. . 3
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9 | 7, 2 | sseldd 3103 |
. . 3
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10 | xrlenlt 7853 |
. . 3
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11 | 8, 9, 10 | syl2anc 409 |
. 2
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12 | simp2r 1009 |
. . . 4
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13 | isof1o 5716 |
. . . . . 6
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14 | f1of 5375 |
. . . . . 6
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15 | 1, 13, 14 | 3syl 17 |
. . . . 5
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16 | 15, 3 | ffvelrnd 5564 |
. . . 4
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17 | 12, 16 | sseldd 3103 |
. . 3
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18 | 15, 2 | ffvelrnd 5564 |
. . . 4
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19 | 12, 18 | sseldd 3103 |
. . 3
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20 | xrlenlt 7853 |
. . 3
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21 | 17, 19, 20 | syl2anc 409 |
. 2
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22 | 6, 11, 21 | 3bitr4d 219 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-f1o 5138 df-fv 5139 df-isom 5140 df-le 7830 |
This theorem is referenced by: seq3coll 10617 summodclem2a 11182 prodmodclem2a 11377 |
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