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Theorem iunxpconst 4937
 Description: Membership in a union of cross products when the second factor is constant. (Contributed by Mario Carneiro, 29-Dec-2014.)
Assertion
Ref Expression
iunxpconst
Distinct variable groups:   ,   ,

Proof of Theorem iunxpconst
StepHypRef Expression
1 xpiundir 4936 . 2
2 iunid 4148 . . 3
32xpeq1i 4901 . 2
41, 3eqtr3i 2460 1
 Colors of variables: wff set class Syntax hints:   wceq 1653  csn 3816  ciun 4095   cxp 4879 This theorem is referenced by:  ralxp  5019  rexxp  5020  mpt2mpt  6168  mpt2mpts  6418  fmpt2  6421  fsumxp  12561  dvfval  19789  indval2  24417  fprodxp  25311  filnetlem3  26422 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-iun 4097  df-opab 4270  df-xp 4887
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