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Theorem opelrn 5239
Description: Membership of second member of an ordered pair in a range. (Contributed by NM, 23-Feb-1997.)
Hypotheses
Ref Expression
brelrn.1
brelrn.2
Assertion
Ref Expression
opelrn

Proof of Theorem opelrn
StepHypRef Expression
1 df-br 4453 . 2
2 brelrn.1 . . 3
3 brelrn.2 . . 3
42, 3brelrn 5238 . 2
51, 4sylbir 213 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818   cvv 3109  <.cop 4035   class class class wbr 4452  rancrn 5005
This theorem is referenced by:  zfrep6  6768  2ndrn  6848  disjen  7694  r0weon  8411  gsum2dlem1  16997  gsum2dlem2  16998  gsum2dOLD  17000  dfres3  29188
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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  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-br 4453  df-opab 4511  df-cnv 5012  df-dm 5014  df-rn 5015
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