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Theorem 2ndrn 6829
 Description: The second ordered pair component of a member of a relation belongs to the range of the relation. (Contributed by NM, 17-Sep-2006.)
Assertion
Ref Expression
2ndrn

Proof of Theorem 2ndrn
StepHypRef Expression
1 1st2nd 6827 . . 3
2 simpr 461 . . 3
31, 2eqeltrrd 2556 . 2
4 fvex 5874 . . 3
5 fvex 5874 . . 3
64, 5opelrn 5232 . 2
73, 6syl 16 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wcel 1767  cop 4033   crn 5000   wrel 5004  cfv 5586  c1st 6779  c2nd 6780 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pow 4625  ax-pr 4686  ax-un 6574 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-opab 4506  df-mpt 4507  df-id 4795  df-xp 5005  df-rel 5006  df-cnv 5007  df-co 5008  df-dm 5009  df-rn 5010  df-iota 5549  df-fun 5588  df-fv 5594  df-1st 6781  df-2nd 6782 This theorem is referenced by:  heicant  29624  mblfinlem1  29626
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