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Theorem brabg2 26417
 Description: Relation by a binary relation abstraction. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypotheses
Ref Expression
brabg2.1
brabg2.2
brabg2.3
brabg2.4
Assertion
Ref Expression
brabg2
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)

Proof of Theorem brabg2
StepHypRef Expression
1 brabg2.3 . . . . 5
21relopabi 5000 . . . 4
32brrelexi 4918 . . 3
4 brabg2.1 . . . . . . 7
5 brabg2.2 . . . . . . 7
64, 5, 1brabg 4474 . . . . . 6
76biimpd 199 . . . . 5
87ex 424 . . . 4
98com3l 77 . . 3
103, 9mpdi 40 . 2
11 brabg2.4 . . 3
124, 5, 1brabg 4474 . . . . 5
1312exbiri 606 . . . 4
1413com3l 77 . . 3
1511, 14mpdi 40 . 2
1610, 15impbid 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  cvv 2956   class class class wbr 4212  copab 4265 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885
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