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Theorem soinxp 4649
 Description: Intersection of linear order with cross product of its field. (Contributed by Mario Carneiro, 10-Jul-2014.)
Assertion
Ref Expression
soinxp

Proof of Theorem soinxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 poinxp 4648 . . 3
2 brinxp 4647 . . . . . . . 8
323adant3 1002 . . . . . . 7
4 brinxp 4647 . . . . . . . . 9
543adant2 1001 . . . . . . . 8
6 brinxp 4647 . . . . . . . . . 10
76ancoms 266 . . . . . . . . 9
873adant1 1000 . . . . . . . 8
95, 8orbi12d 783 . . . . . . 7
103, 9imbi12d 233 . . . . . 6
11103expb 1183 . . . . 5
12112ralbidva 2476 . . . 4
1312ralbiia 2468 . . 3
141, 13anbi12i 456 . 2
15 df-iso 4252 . 2
16 df-iso 4252 . 2
1714, 15, 163bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wo 698   w3a 963   wcel 2125  wral 2432   cin 3097   class class class wbr 3961   wpo 4249   wor 4250   cxp 4577 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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130  ax-pr 4164 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-un 3102  df-in 3104  df-ss 3111  df-pw 3541  df-sn 3562  df-pr 3563  df-op 3565  df-br 3962  df-opab 4022  df-po 4251  df-iso 4252  df-xp 4585 This theorem is referenced by: (None)
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