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Theorem rexrab2 2731
 Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
rexrab2
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem rexrab2
StepHypRef Expression
1 df-rab 2332 . . 3
21rexeqi 2527 . 2
3 ralab2.1 . . 3
43rexab2 2730 . 2
5 anass 387 . . . 4
65exbii 1512 . . 3
7 df-rex 2329 . . 3
86, 7bitr4i 180 . 2
92, 4, 83bitri 199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102  wex 1397   wcel 1409  cab 2042  wrex 2324  crab 2327 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-rab 2332 This theorem is referenced by: (None)
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