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Theorem unixpm 5074
 Description: The double class union of an inhabited cross product is the union of its members. (Contributed by Jim Kingdon, 18-Dec-2018.)
Assertion
Ref Expression
unixpm
Distinct variable groups:   ,   ,

Proof of Theorem unixpm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 relxp 4648 . . 3
2 relfld 5067 . . 3
31, 2ax-mp 5 . 2
4 ancom 264 . . . 4
5 xpm 4960 . . . 4
64, 5bitri 183 . . 3
7 dmxpm 4759 . . . 4
8 rnxpm 4968 . . . 4
9 uneq12 3225 . . . 4
107, 8, 9syl2an 287 . . 3
116, 10sylbir 134 . 2
123, 11syl5eq 2184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331  wex 1468   wcel 1480   cun 3069  cuni 3736   cxp 4537   cdm 4539   crn 4540   wrel 4544 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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546  df-cnv 4547  df-dm 4549  df-rn 4550 This theorem is referenced by: (None)
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