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Theorem brimralrspcev 3987
 Description: Restricted existential specialization with a restricted universal quantifier over an implication with a relation in the antecedent, closed form. (Contributed by AV, 20-Aug-2022.)
Assertion
Ref Expression
brimralrspcev
Distinct variable groups:   ,   ,,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem brimralrspcev
StepHypRef Expression
1 breq2 3933 . . 3
21anbi2d 459 . 2
32rspceaimv 2797 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wcel 1480  wral 2416  wrex 2417   class class class wbr 3929 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930 This theorem is referenced by:  dveflem  12864
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