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Bibliographic Cross-References
 
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Bibliographic Cross-References   This table collects in one place the bibliographic references made in the Intuitionistic Logic Explorer's axiom, definition, and theorem Descriptions. If you are studying a particular reference, this list can be handy for finding out where any corresponding Metamath theorems might be located. Keep in mind that we usually give only one reference for a theorem that may appear in several books, so it can also be useful to browse the Related Theorems around a theorem of interest.

Bibliographic Cross-Reference for the Higher-Order Logic Explorer
Bibliographic Reference DescriptionHigher-Order Logic Explorer Page(s)
[BellMachover] p. 36Lemma 10.3id1 19
[BellMachover] p. 97Definition 10.1df-eu 1694
[BellMachover] p. 460Notationdf-mo 1695
[BellMachover] p. 460Definitionmo3 1715
[Hamilton] p. 28Definition 2.1ax-1 5
[Hamilton] p. 31Example 2.7(a)id1 19
[Hamilton] p. 73Rule 1ax-mp 8
[Hamilton] p. 74Rule 2ax-gen 1257
[KalishMontague] p. 81Axiom B7' in footnote 1ax-i9 1321
[Kunen] p. 10Axiom 0a9e 1436
[Margaris] p. 40Rule Cexlimiv 1612
[Margaris] p. 49Axiom A1ax-1 5
[Margaris] p. 49Axiom A2ax-2 6
[Margaris] p. 49Axiom A3ax-3 7
[Margaris] p. 49Definitiondf-ex 1299  df-or 787  dfbi2 366
[Margaris] p. 51Theorem 1id1 19
[Margaris] p. 56Theorem 3syld 39
[Margaris] p. 60Theorem 8mth8 557
[Margaris] p. 89Theorem 19.219.2 1409
[Margaris] p. 89Theorem 19.319.3 1354
[Margaris] p. 89Theorem 19.5alcom 1276
[Margaris] p. 89Theorem 19.6alex 1689
[Margaris] p. 89Theorem 19.7alnex 1298
[Margaris] p. 89Theorem 19.819.8a 1372
[Margaris] p. 89Theorem 19.919.9 1411  19.9v 1600
[Margaris] p. 89Theorem 19.11excom 1414  excomim 1413
[Margaris] p. 89Theorem 19.1219.12 1415
[Margaris] p. 90Theorem 19.14exnal 1777
[Margaris] p. 90Theorem 19.15albi 1269
[Margaris] p. 90Theorem 19.1619.16 1355
[Margaris] p. 90Theorem 19.1719.17 1356
[Margaris] p. 90Theorem 19.18exbi 1380
[Margaris] p. 90Theorem 19.1919.19 1416
[Margaris] p. 90Theorem 19.20alim 1265  alimd 1268  alimdv 1606
[Margaris] p. 90Theorem 19.2119.21-2 1358  19.21 1357  19.21bi 1360  19.21t 1370  19.21v 1601  alrimd 1277  alrimdv 1604  alrimi 1270  alrimiv 1602  alrimivv 1603
[Margaris] p. 90Theorem 19.222alimdv 1608  2eximdv 1609  exim 1376  eximd 1385  eximdv 1607
[Margaris] p. 90Theorem 19.2319.23 1297  19.23bi 1373  19.23t 1296  19.23v 1610  19.23vv 1611  exlimd 1375  exlimdv 1529  exlimdvv 1615  exlimi 1374  exlimiv 1612  exlimivv 1614
[Margaris] p. 90Theorem 19.2419.24 1422
[Margaris] p. 90Theorem 19.2519.25 1399
[Margaris] p. 90Theorem 19.2619.26-2 1281  19.26-3an 1282  19.26 1279
[Margaris] p. 90Theorem 19.2719.27 1362  19.27v 1616
[Margaris] p. 90Theorem 19.2819.28 1363  19.28v 1617
[Margaris] p. 90Theorem 19.2919.29 1390  19.29r 1391  19.29r2 1392  19.29x 1393
[Margaris] p. 90Theorem 19.3019.30 1782
[Margaris] p. 90Theorem 19.3119.31 1365
[Margaris] p. 90Theorem 19.3219.32 1364
[Margaris] p. 90Theorem 19.3319.33 1283  19.33b 1783  19.33b2 1401
[Margaris] p. 90Theorem 19.3419.34 1425
[Margaris] p. 90Theorem 19.3519.35-1 1394  19.35 1395  19.35i 1397  19.35ri 1398
[Margaris] p. 90Theorem 19.3619.36 1417  19.36aiv 1619  19.36i 1418  19.36v 1618
[Margaris] p. 90Theorem 19.3719.37 1419  19.37aiv 1622  19.37v 1621
[Margaris] p. 90Theorem 19.3819.38 1420
[Margaris] p. 90Theorem 19.3919.39 1421
[Margaris] p. 90Theorem 19.4019.40-2 1403  19.40 1402
[Margaris] p. 90Theorem 19.4119.41 1426  19.41v 1623  19.41vv 1624  19.41vvv 1625  19.41vvvv 1626
[Margaris] p. 90Theorem 19.4219.42 1427  19.42v 1627  19.42vv 1629  19.42vvv 1630
[Margaris] p. 90Theorem 19.4319.43 1400
[Margaris] p. 90Theorem 19.4419.44 1423
[Margaris] p. 90Theorem 19.4519.45 1424
[Margaris] p. 110Exercise 2(b)eu1 1705
[Megill] p. 444Axiom C5ax-17 1319
[Megill] p. 445Lemma L12alequcom 1316  ax-10 1306
[Megill] p. 446Lemma L17equtrr 1447
[Megill] p. 446Lemma L18ax9 1439
[Megill] p. 446Lemma L19hbnae 1459
[Megill] p. 447Remark 9.1df-sb 1485  sbid 1497
[Megill] p. 448Remark 9.6ax15 1685
[Megill] p. 448Scheme C4'ax-5o 1328
[Megill] p. 448Scheme C5'ax-4 1310
[Megill] p. 448Scheme C6'ax-7 1256
[Megill] p. 448Scheme C7'ax-6o 1331
[Megill] p. 448Scheme C8'ax-8 1305
[Megill] p. 448Scheme C9'ax-i12 1309
[Megill] p. 448Scheme C10'ax-9o 1438  ax-i9 1321
[Megill] p. 448Scheme C11'ax-10o 1455
[Megill] p. 448Scheme C12'ax-13 1313
[Megill] p. 448Scheme C13'ax-14 1314
[Megill] p. 448Scheme C14'ax-15 1686
[Megill] p. 448Scheme C15'ax-11o 1533
[Megill] p. 448Scheme C16'ax-16 1523
[Megill] p. 448Theorem 9.4dral1 1465  dral2 1466  drex1 1467  drex2 1468  drsb1 1488  drsb2 1545
[Megill] p. 449Theorem 9.7sbcom2 1661  sbequ 1544  sbid2v 1669
[Megill] p. 450Example in Appendixhba1 1339
[Mendelson] p. 36Lemma 1.8id1 19
[Mendelson] p. 69Axiom 4stdpc4 1498
[Mendelson] p. 69Axiom 5ax-5o 1328  stdpc5 1359
[Mendelson] p. 81Rule Cexlimiv 1612
[Mendelson] p. 95Axiom 6stdpc6 1442
[Mendelson] p. 95Axiom 7stdpc7 1493
[Monk2] p. 105Axiom C4ax-5 1254
[Monk2] p. 105Axiom C7ax-8 1305
[Monk2] p. 105Axiom C8ax-11 1307  ax-11o 1533
[Monk2] p. 105Axiom (C8)ax11v 1582
[Monk2] p. 108Lemma 5ax-5o 1328
[Monk2] p. 109Lemma 12ax-7 1256
[Monk2] p. 109Lemma 15equvin 1591  equvini 1481
[Monk2] p. 113Axiom C5-1ax-17 1319
[Monk2] p. 113Axiom C5-2ax-6 1255
[Monk2] p. 113Axiom C5-3ax-7 1256
[Monk2] p. 114Lemma 21ax4 1326
[Monk2] p. 114Lemma 22ax5o 1327  hba1 1339
[Monk2] p. 114Lemma 23hbia1 1349
[Monk2] p. 114Lemma 24hba2 1348
[Quine] p. 17Definition 2.1''dfsb7 1666
[Quine] p. 40Theorem 6.1sb5 1585
[Quine] p. 40Theorem 6.2sb56 1583  sb6 1584
[Stoll] p. 176Theorem 3.4(27)iman 777
[TakeutiZaring] p. 26Definition 6.10eu2 1709
[TakeutiZaring] p. 53Proposition 7.532eu5 1769
[Tarski] p. 67Axiom B5ax-4 1310
[Tarski] p. 68Lemma 6equid 1441  equid1 1440
[Tarski] p. 69Lemma 7equcomi 1443
[Tarski] p. 70Lemma 14a4im 1471  a4ime 1472
[Tarski] p. 70Lemma 16ax-11 1307  ax-11o 1533  ax11i 1453
[Tarski] p. 70Lemmas 16 and 17sb6 1584
[Tarski] p. 77Axiom B6 (p. 75) of system S2ax-17 1319
[Tarski] p. 77Axiom B8 (p. 75) of system S2ax-13 1313  ax-14 1314
[WhiteheadRussell] p. 96Axiom *1.3olc 608
[WhiteheadRussell] p. 96Axiom *1.4pm1.4 621
[WhiteheadRussell] p. 96Axiom *1.2 (Taut)pm1.2 648
[WhiteheadRussell] p. 96Axiom *1.5 (Assoc)pm1.5 657
[WhiteheadRussell] p. 97Axiom *1.6 (Sum)orim2 678
[WhiteheadRussell] p. 100Theorem *2.01pm2.01 528
[WhiteheadRussell] p. 100Theorem *2.02ax-1 5
[WhiteheadRussell] p. 100Theorem *2.03con2 550
[WhiteheadRussell] p. 100Theorem *2.04pm2.04 75
[WhiteheadRussell] p. 100Theorem *2.05imim2 48
[WhiteheadRussell] p. 100Theorem *2.06imim1 69
[WhiteheadRussell] p. 101Theorem *2.1pm2.1 797
[WhiteheadRussell] p. 101Theorem *2.06syl 14
[WhiteheadRussell] p. 101Theorem *2.07pm2.07 631
[WhiteheadRussell] p. 101Theorem *2.08id 18  id1 19
[WhiteheadRussell] p. 101Theorem *2.11exmid 796
[WhiteheadRussell] p. 101Theorem *2.12notnot1 540
[WhiteheadRussell] p. 101Theorem *2.13pm2.13 798
[WhiteheadRussell] p. 102Theorem *2.14notnot2 717
[WhiteheadRussell] p. 102Theorem *2.15con1 720
[WhiteheadRussell] p. 103Theorem *2.16con3 549
[WhiteheadRussell] p. 103Theorem *2.17ax-3 7
[WhiteheadRussell] p. 103Theorem *2.18pm2.18 715
[WhiteheadRussell] p. 104Theorem *2.2orc 609
[WhiteheadRussell] p. 104Theorem *2.3pm2.3 667
[WhiteheadRussell] p. 104Theorem *2.21pm2.21 529
[WhiteheadRussell] p. 104Theorem *2.24pm2.24 532
[WhiteheadRussell] p. 104Theorem *2.25pm2.25 790
[WhiteheadRussell] p. 104Theorem *2.26pm2.26 825
[WhiteheadRussell] p. 104Theorem *2.27pm2.27 34
[WhiteheadRussell] p. 104Theorem *2.31pm2.31 660
[WhiteheadRussell] p. 105Theorem *2.32pm2.32 661
[WhiteheadRussell] p. 105Theorem *2.36pm2.36 691
[WhiteheadRussell] p. 105Theorem *2.37pm2.37 692
[WhiteheadRussell] p. 105Theorem *2.38pm2.38 690
[WhiteheadRussell] p. 105Definition *2.33df-3or 883
[WhiteheadRussell] p. 106Theorem *2.4pm2.4 670
[WhiteheadRussell] p. 106Theorem *2.41pm2.41 668
[WhiteheadRussell] p. 106Theorem *2.42pm2.42 669
[WhiteheadRussell] p. 106Theorem *2.43pm2.43 46
[WhiteheadRussell] p. 106Theorem *2.45pm2.45 632
[WhiteheadRussell] p. 106Theorem *2.46pm2.46 633
[WhiteheadRussell] p. 107Theorem *2.5pm2.5 752
[WhiteheadRussell] p. 107Theorem *2.6pm2.6 740
[WhiteheadRussell] p. 107Theorem *2.47pm2.47 634
[WhiteheadRussell] p. 107Theorem *2.48pm2.48 635
[WhiteheadRussell] p. 107Theorem *2.49pm2.49 636
[WhiteheadRussell] p. 107Theorem *2.51pm2.51 559
[WhiteheadRussell] p. 107Theorem *2.52pm2.52 560
[WhiteheadRussell] p. 107Theorem *2.53pm2.53 616
[WhiteheadRussell] p. 107Theorem *2.54pm2.54 786
[WhiteheadRussell] p. 107Theorem *2.55orel1 619
[WhiteheadRussell] p. 107Theorem *2.56orel2 620
[WhiteheadRussell] p. 107Theorem *2.61pm2.61 741
[WhiteheadRussell] p. 107Theorem *2.62pm2.62 642
[WhiteheadRussell] p. 107Theorem *2.63pm2.63 687
[WhiteheadRussell] p. 107Theorem *2.64pm2.64 688
[WhiteheadRussell] p. 107Theorem *2.65pm2.65 563
[WhiteheadRussell] p. 107Theorem *2.67pm2.67-2 610  pm2.67 637
[WhiteheadRussell] p. 107Theorem *2.521pm2.521 753
[WhiteheadRussell] p. 107Theorem *2.621pm2.621 641
[WhiteheadRussell] p. 108Theorem *2.8pm2.8 697
[WhiteheadRussell] p. 108Theorem *2.68pm2.68 791
[WhiteheadRussell] p. 108Theorem *2.69looinv 755
[WhiteheadRussell] p. 108Theorem *2.73pm2.73 693
[WhiteheadRussell] p. 108Theorem *2.74pm2.74 694
[WhiteheadRussell] p. 108Theorem *2.75pm2.75 696
[WhiteheadRussell] p. 108Theorem *2.76pm2.76 695
[WhiteheadRussell] p. 108Theorem *2.77ax-2 6
[WhiteheadRussell] p. 108Theorem *2.81pm2.81 698
[WhiteheadRussell] p. 108Theorem *2.82pm2.82 699
[WhiteheadRussell] p. 108Theorem *2.83pm2.83 70
[WhiteheadRussell] p. 108Theorem *2.85pm2.85 819
[WhiteheadRussell] p. 108Theorem *2.86pm2.86 93
[WhiteheadRussell] p. 111Theorem *3.1pm3.1 646
[WhiteheadRussell] p. 111Theorem *3.2pm3.2 125
[WhiteheadRussell] p. 111Theorem *3.11pm3.11 812
[WhiteheadRussell] p. 111Theorem *3.12pm3.12 813
[WhiteheadRussell] p. 111Theorem *3.13pm3.13 814
[WhiteheadRussell] p. 111Theorem *3.14pm3.14 645
[WhiteheadRussell] p. 111Theorem *3.21pm3.21 250
[WhiteheadRussell] p. 111Theorem *3.22pm3.22 251
[WhiteheadRussell] p. 111Theorem *3.24pm3.24 604
[WhiteheadRussell] p. 112Theorem *3.35pm3.35 327
[WhiteheadRussell] p. 112Theorem *3.3 (Exp)pm3.3 247
[WhiteheadRussell] p. 112Theorem *3.31 (Imp)pm3.31 248
[WhiteheadRussell] p. 112Theorem *3.26 (Simp)simpl 101  simplim 730
[WhiteheadRussell] p. 112Theorem *3.27 (Simp)simpr 102  simprim 729
[WhiteheadRussell] p. 112Theorem *3.33 (Syll)pm3.33 325
[WhiteheadRussell] p. 112Theorem *3.34 (Syll)pm3.34 326
[WhiteheadRussell] p. 112Theorem *3.37 (Transp)pm3.37 782
[WhiteheadRussell] p. 113Theorem *3.4pm3.4 315
[WhiteheadRussell] p. 113Theorem *3.41pm3.41 313
[WhiteheadRussell] p. 113Theorem *3.42pm3.42 314
[WhiteheadRussell] p. 113Theorem *3.44jao 647  pm3.44 611
[WhiteheadRussell] p. 113Theorem *3.47prth 324
[WhiteheadRussell] p. 113Theorem *3.43 (Comp)pm3.43 515
[WhiteheadRussell] p. 113Theorem *3.45 (Fact)pm3.45 510
[WhiteheadRussell] p. 114Theorem *3.48pm3.48 674
[WhiteheadRussell] p. 116Theorem *4.1con34b 756
[WhiteheadRussell] p. 117Theorem *4.2biid 159
[WhiteheadRussell] p. 117Theorem *4.11notbi 759
[WhiteheadRussell] p. 117Theorem *4.12con2bi 760
[WhiteheadRussell] p. 117Theorem *4.13notnot 757
[WhiteheadRussell] p. 117Theorem *4.14pm4.14 781
[WhiteheadRussell] p. 117Theorem *4.15pm4.15 783
[WhiteheadRussell] p. 117Theorem *4.21bicom 127
[WhiteheadRussell] p. 117Theorem *4.22biantr 862  bitr 439
[WhiteheadRussell] p. 117Theorem *4.24pm4.24 372
[WhiteheadRussell] p. 117Theorem *4.25oridm 649  pm4.25 650
[WhiteheadRussell] p. 118Theorem *4.3ancom 252
[WhiteheadRussell] p. 118Theorem *4.4andi 706
[WhiteheadRussell] p. 118Theorem *4.31orcom 622
[WhiteheadRussell] p. 118Theorem *4.32anass 380
[WhiteheadRussell] p. 118Theorem *4.33orass 659
[WhiteheadRussell] p. 118Theorem *4.36anbi1 437
[WhiteheadRussell] p. 118Theorem *4.37orbi1 681
[WhiteheadRussell] p. 118Theorem *4.38pm4.38 519
[WhiteheadRussell] p. 118Theorem *4.39pm4.39 710
[WhiteheadRussell] p. 118Definition *4.34df-3an 884
[WhiteheadRussell] p. 119Theorem *4.41ordi 704
[WhiteheadRussell] p. 119Theorem *4.43pm4.43 858
[WhiteheadRussell] p. 119Theorem *4.44pm4.44 671
[WhiteheadRussell] p. 119Theorem *4.45orabs 701  pm4.45 673  pm4.45im 316
[WhiteheadRussell] p. 119Theorem *10.2219.26 1279
[WhiteheadRussell] p. 120Theorem *4.5anor 802
[WhiteheadRussell] p. 120Theorem *4.6imor 794
[WhiteheadRussell] p. 120Theorem *4.7anclb 301
[WhiteheadRussell] p. 120Theorem *4.51ianor 801
[WhiteheadRussell] p. 120Theorem *4.52pm4.52 804
[WhiteheadRussell] p. 120Theorem *4.53pm4.53 805
[WhiteheadRussell] p. 120Theorem *4.54pm4.54 806
[WhiteheadRussell] p. 120Theorem *4.55pm4.55 808
[WhiteheadRussell] p. 120Theorem *4.56ioran 644  pm4.56 809
[WhiteheadRussell] p. 120Theorem *4.57oran 810  pm4.57 811
[WhiteheadRussell] p. 120Theorem *4.61pm4.61 779
[WhiteheadRussell] p. 120Theorem *4.62pm4.62 799
[WhiteheadRussell] p. 120Theorem *4.63pm4.63 774
[WhiteheadRussell] p. 120Theorem *4.64pm4.64 793
[WhiteheadRussell] p. 120Theorem *4.65pm4.65 780
[WhiteheadRussell] p. 120Theorem *4.66pm4.66 800
[WhiteheadRussell] p. 120Theorem *4.67pm4.67 775
[WhiteheadRussell] p. 120Theorem *4.71pm4.71 367  pm4.71i 369  pm4.71r 368  pm4.71rd 371  pm4.71ri 370
[WhiteheadRussell] p. 121Theorem *4.72pm4.72 711
[WhiteheadRussell] p. 121Theorem *4.73iba 283
[WhiteheadRussell] p. 121Theorem *4.74biorf 638
[WhiteheadRussell] p. 121Theorem *4.76jcab 516  pm4.76 518
[WhiteheadRussell] p. 121Theorem *4.77jaob 607  pm4.77 686
[WhiteheadRussell] p. 121Theorem *4.78pm4.78 815
[WhiteheadRussell] p. 121Theorem *4.79pm4.79 816
[WhiteheadRussell] p. 122Theorem *4.8pm4.8 601
[WhiteheadRussell] p. 122Theorem *4.81pm4.81 1776
[WhiteheadRussell] p. 122Theorem *4.82pm4.82 859
[WhiteheadRussell] p. 122Theorem *4.83pm4.83 860
[WhiteheadRussell] p. 122Theorem *4.84imbi1 224
[WhiteheadRussell] p. 122Theorem *4.85imbi2 225
[WhiteheadRussell] p. 122Theorem *4.86bibi1 228
[WhiteheadRussell] p. 122Theorem *4.87bi2.04 236  impexp 249  pm4.87 475
[WhiteheadRussell] p. 123Theorem *5.1pm5.1 514
[WhiteheadRussell] p. 123Theorem *5.11pm5.11 826
[WhiteheadRussell] p. 123Theorem *5.12pm5.12 827
[WhiteheadRussell] p. 123Theorem *5.13pm5.13 829
[WhiteheadRussell] p. 123Theorem *5.14pm5.14 828
[WhiteheadRussell] p. 124Theorem *5.15pm5.15 830
[WhiteheadRussell] p. 124Theorem *5.16pm5.16 712
[WhiteheadRussell] p. 124Theorem *5.17pm5.17 817
[WhiteheadRussell] p. 124Theorem *5.18nbbn 771  pm5.18 769
[WhiteheadRussell] p. 124Theorem *5.19pm5.19 600
[WhiteheadRussell] p. 124Theorem *5.21pm5.21 589
[WhiteheadRussell] p. 124Theorem *5.22xor 820
[WhiteheadRussell] p. 124Theorem *5.23dfbi3 822
[WhiteheadRussell] p. 124Theorem *5.24pm5.24 823
[WhiteheadRussell] p. 124Theorem *5.25dfor2 792
[WhiteheadRussell] p. 125Theorem *5.3pm5.3 441
[WhiteheadRussell] p. 125Theorem *5.4pm5.4 237
[WhiteheadRussell] p. 125Theorem *5.5pm5.5 230
[WhiteheadRussell] p. 125Theorem *5.6pm5.6 838
[WhiteheadRussell] p. 125Theorem *5.7pm5.7 865
[WhiteheadRussell] p. 125Theorem *5.31pm5.31 328
[WhiteheadRussell] p. 125Theorem *5.32pm5.32 426
[WhiteheadRussell] p. 125Theorem *5.33pm5.33 523
[WhiteheadRussell] p. 125Theorem *5.35pm5.35 833
[WhiteheadRussell] p. 125Theorem *5.36pm5.36 524
[WhiteheadRussell] p. 125Theorem *5.41imdi 238  pm5.41 239
[WhiteheadRussell] p. 125Theorem *5.42pm5.42 302
[WhiteheadRussell] p. 125Theorem *5.44pm5.44 837
[WhiteheadRussell] p. 125Theorem *5.53pm5.53 689
[WhiteheadRussell] p. 125Theorem *5.54pm5.54 834
[WhiteheadRussell] p. 125Theorem *5.55pm5.55 831
[WhiteheadRussell] p. 125Theorem *5.61pm5.61 683
[WhiteheadRussell] p. 125Theorem *5.62pm5.62 854
[WhiteheadRussell] p. 125Theorem *5.63pm5.63 855
[WhiteheadRussell] p. 125Theorem *5.71pm5.71 867
[WhiteheadRussell] p. 125Theorem *5.501pm5.501 232
[WhiteheadRussell] p. 126Theorem *5.74pm5.74 167
[WhiteheadRussell] p. 126Theorem *5.75pm5.75 868
[WhiteheadRussell] p. 159Theorem *11.07pm11.07 1662
[WhiteheadRussell] p. 160Theorem *11.21alrot3 1284
[WhiteheadRussell] p. 163Theorem *11.4219.40-2 1403
[WhiteheadRussell] p. 164Theorem *11.52nalexn 1778
[WhiteheadRussell] p. 164Theorem *11.512exnexn 1780
[WhiteheadRussell] p. 164Theorem *11.53pm11.53 1613
[WhiteheadRussell] p. 175Definition *14.02df-eu 1694
[WhiteheadRussell] p. 192Theorem *14.26eupick 1748  eupickbi 1751

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