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Theorem xp2dju 7091
 Description: Two times a cardinal number. Exercise 4.56(g) of [Mendelson] p. 258. (Contributed by NM, 27-Sep-2004.) (Revised by Mario Carneiro, 29-Apr-2015.)
Assertion
Ref Expression
xp2dju

Proof of Theorem xp2dju
StepHypRef Expression
1 xpundir 4605 . 2
2 df2o3 6336 . . . 4
3 df-pr 3540 . . . 4
42, 3eqtri 2161 . . 3
54xpeq1i 4568 . 2
6 df-dju 6933 . 2
71, 5, 63eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wceq 1332   cun 3075  c0 3369  csn 3533  cpr 3534   cxp 4546  c1o 6315  c2o 6316   ⊔ cdju 6932 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-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-dif 3079  df-un 3081  df-nul 3370  df-pr 3540  df-opab 3999  df-suc 4302  df-xp 4554  df-1o 6322  df-2o 6323  df-dju 6933 This theorem is referenced by: (None)
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