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Theorem ovanraleqv 5802
 Description: Equality theorem for a conjunction with an operation values within a restricted universal quantification. Technical theorem to be used to reduce the size of a significant number of proofs. (Contributed by AV, 13-Aug-2022.)
Hypothesis
Ref Expression
ovanraleqv.1
Assertion
Ref Expression
ovanraleqv
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem ovanraleqv
StepHypRef Expression
1 ovanraleqv.1 . . 3
2 oveq2 5786 . . . 4
32eqeq1d 2149 . . 3
41, 3anbi12d 465 . 2
54ralbidv 2438 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332  wral 2417  (class class class)co 5778 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2689  df-un 3076  df-sn 3534  df-pr 3535  df-op 3537  df-uni 3741  df-br 3934  df-iota 5092  df-fv 5135  df-ov 5781 This theorem is referenced by: (None)
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