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Mirrors > Home > ILE Home > Th. List > leisorel | Unicode version |
Description: Version of isorel 5825 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 999 |
. . 3
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2 | simp3r 1028 |
. . 3
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3 | simp3l 1027 |
. . 3
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4 | isorel 5825 |
. . . 4
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5 | 4 | notbid 668 |
. . 3
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6 | 1, 2, 3, 5 | syl12anc 1247 |
. 2
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7 | simp2l 1025 |
. . . 4
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8 | 7, 3 | sseldd 3171 |
. . 3
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9 | 7, 2 | sseldd 3171 |
. . 3
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10 | xrlenlt 8040 |
. . 3
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11 | 8, 9, 10 | syl2anc 411 |
. 2
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12 | simp2r 1026 |
. . . 4
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13 | isof1o 5824 |
. . . . . 6
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14 | f1of 5476 |
. . . . . 6
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15 | 1, 13, 14 | 3syl 17 |
. . . . 5
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16 | 15, 3 | ffvelcdmd 5668 |
. . . 4
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17 | 12, 16 | sseldd 3171 |
. . 3
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18 | 15, 2 | ffvelcdmd 5668 |
. . . 4
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19 | 12, 18 | sseldd 3171 |
. . 3
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20 | xrlenlt 8040 |
. . 3
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21 | 17, 19, 20 | syl2anc 411 |
. 2
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22 | 6, 11, 21 | 3bitr4d 220 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-iota 5193 df-fun 5233 df-fn 5234 df-f 5235 df-f1 5236 df-f1o 5238 df-fv 5239 df-isom 5240 df-le 8016 |
This theorem is referenced by: seq3coll 10840 summodclem2a 11407 prodmodclem2a 11602 |
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