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Theorem brab1 3984
 Description: Relationship between a binary relation and a class abstraction. (Contributed by Andrew Salmon, 8-Jul-2011.)
Assertion
Ref Expression
brab1
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem brab1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2693 . . 3
2 breq1 3941 . . . 4
3 breq1 3941 . . . 4
42, 3sbcie2g 2947 . . 3
51, 4ax-mp 5 . 2
6 df-sbc 2915 . 2
75, 6bitr3i 185 1
 Colors of variables: wff set class Syntax hints:   wb 104   wcel 1481  cab 2126  cvv 2690  wsbc 2914   class class class wbr 3938 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-v 2692  df-sbc 2915  df-un 3081  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939 This theorem is referenced by: (None)
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