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Theorem raliunxp 5147
 Description: Write a double restricted quantification as one universal quantifier. In this version of ralxp 5149, ( ) is not assumed to be constant. (Contributed by Mario Carneiro, 29-Dec-2014.)
Hypothesis
Ref Expression
ralxp.1
Assertion
Ref Expression
raliunxp
Distinct variable groups:   ,,,   ,,   ,,   ,

Proof of Theorem raliunxp
StepHypRef Expression
1 eliunxp 5145 . . . . . 6
21imbi1i 325 . . . . 5
3 19.23vv 1761 . . . . 5
42, 3bitr4i 252 . . . 4
54albii 1640 . . 3
6 alrot3 1846 . . . 4
7 impexp 446 . . . . . . 7
87albii 1640 . . . . . 6
9 opex 4716 . . . . . . 7
10 ralxp.1 . . . . . . . 8
1110imbi2d 316 . . . . . . 7
129, 11ceqsalv 3137 . . . . . 6
138, 12bitri 249 . . . . 5
14132albii 1641 . . . 4
156, 14bitri 249 . . 3
165, 15bitri 249 . 2
17 df-ral 2812 . 2
18 r2al 2835 . 2
1916, 17, 183bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  A.wral 2807  {csn 4029  <.cop 4035  U_ciun 4330  X.cxp 5002 This theorem is referenced by:  rexiunxp  5148  ralxp  5149  fmpt2x  6866  ovmptss  6881  filnetlem4  30199 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-iun 4332  df-opab 4511  df-xp 5010  df-rel 5011
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