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Theorem brab1 4249
 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 2951 . . 3
2 breq1 4207 . . . 4
3 breq1 4207 . . . 4
42, 3sbcie2g 3186 . . 3
51, 4ax-mp 8 . 2
6 df-sbc 3154 . 2
75, 6bitr3i 243 1
 Colors of variables: wff set class Syntax hints:   wb 177   wcel 1725  cab 2421  cvv 2948  wsbc 3153   class class class wbr 4204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205
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