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Theorem rspceov 5578
 Description: A frequently used special case of rspc2ev 2716 for operation values. (Contributed by NM, 21-Mar-2007.)
Assertion
Ref Expression
rspceov
Distinct variable groups:   ,   ,,   ,,   ,   ,,   ,,
Allowed substitution hints:   ()   ()

Proof of Theorem rspceov
StepHypRef Expression
1 oveq1 5550 . . 3
21eqeq2d 2093 . 2
3 oveq2 5551 . . 3
43eqeq2d 2093 . 2
52, 4rspc2ev 2716 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 920   wceq 1285   wcel 1434  wrex 2350  (class class class)co 5543 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-un 2978  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-br 3794  df-iota 4897  df-fv 4940  df-ov 5546 This theorem is referenced by:  genpprecll  6766  genppreclu  6767  elz2  8500  znq  8790  qaddcl  8801  qmulcl  8803  qreccl  8808
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