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Theorem ralunb 3152
 Description: Restricted quantification over a union. (Contributed by Scott Fenton, 12-Apr-2011.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
ralunb

Proof of Theorem ralunb
StepHypRef Expression
1 elun 3112 . . . . . 6
21imbi1i 231 . . . . 5
3 jaob 641 . . . . 5
42, 3bitri 177 . . . 4
54albii 1375 . . 3
6 19.26 1386 . . 3
75, 6bitri 177 . 2
8 df-ral 2328 . 2
9 df-ral 2328 . . 3
10 df-ral 2328 . . 3
119, 10anbi12i 441 . 2
127, 8, 113bitr4i 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wo 639  wal 1257   wcel 1409  wral 2323   cun 2943 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-ral 2328  df-v 2576  df-un 2950 This theorem is referenced by:  ralun  3153  ralprg  3449  raltpg  3451  ralunsn  3596  rexfiuz  9816
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