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Theorem opeluu 4707
 Description: Each member of an ordered pair belongs to the union of the union of a class to which the ordered pair belongs. Lemma 3D of [Enderton] p. 41. (Contributed by NM, 31-Mar-1995.) (Revised by Mario Carneiro, 27-Feb-2016.)
Hypotheses
Ref Expression
opeluu.1
opeluu.2
Assertion
Ref Expression
opeluu

Proof of Theorem opeluu
StepHypRef Expression
1 opeluu.1 . . . 4
21prid1 3904 . . 3
3 opeluu.2 . . . . 5
41, 3opi2 4423 . . . 4
5 elunii 4012 . . . 4
64, 5mpan 652 . . 3
7 elunii 4012 . . 3
82, 6, 7sylancr 645 . 2
93prid2 3905 . . 3
10 elunii 4012 . . 3
119, 6, 10sylancr 645 . 2
128, 11jca 519 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wcel 1725  cvv 2948  cpr 3807  cop 3809  cuni 4007 This theorem is referenced by:  asymref  5242  asymref2  5243  wrdexb  11755 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008
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