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Theorem opelxp2 4941
Description: The second member of an ordered pair of classes in a cross product belongs to second cross product argument. (Contributed by Mario Carneiro, 26-Apr-2015.)
Assertion
Ref Expression
opelxp2  |-  ( <. A ,  B >.  e.  ( C  X.  D
)  ->  B  e.  D )

Proof of Theorem opelxp2
StepHypRef Expression
1 opelxp 4937 . 2  |-  ( <. A ,  B >.  e.  ( C  X.  D
)  <->  ( A  e.  C  /\  B  e.  D ) )
21simprbi 452 1  |-  ( <. A ,  B >.  e.  ( C  X.  D
)  ->  B  e.  D )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1727   <.cop 3841    X. cxp 4905
This theorem is referenced by:  dff4  5912  eceqoveq  7038  isfin4-3  8226  axdc4lem  8366  canthp1lem2  8559  txcmplem1  17704  txlm  17711  nvex  22121  pprodss4v  25760  brcgr  25870
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 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432
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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-opab 4292  df-xp 4913
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