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Theorem copsex2gb 5118
Description: Implicit substitution inference for ordered pairs. Compare copsex2ga 5119. (Contributed by NM, 12-Mar-2014.)
Hypothesis
Ref Expression
copsex2ga.1
Assertion
Ref Expression
copsex2gb
Distinct variable groups:   , ,   , ,

Proof of Theorem copsex2gb
StepHypRef Expression
1 elvv 5063 . . 3
21anbi1i 695 . 2
3 19.41vv 1772 . 2
4 copsex2ga.1 . . . 4
54pm5.32i 637 . . 3
652exbii 1668 . 2
72, 3, 63bitr2ri 274 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109  <.cop 4035  X.cxp 5002
This theorem is referenced by:  copsex2ga  5119  elopaba  5120
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010
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