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Theorem raliunxp 5015
 Description: Write a double restricted quantification as one universal quantifier. In this version of ralxp 5017, 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:   ,,,   ,,   ,,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem raliunxp
StepHypRef Expression
1 eliunxp 5013 . . . . . 6
21imbi1i 317 . . . . 5
3 19.23vv 1916 . . . . 5
42, 3bitr4i 245 . . . 4
54albii 1576 . . 3
6 alrot3 1754 . . . 4
7 impexp 435 . . . . . . 7
87albii 1576 . . . . . 6
9 opex 4428 . . . . . . 7
10 ralxp.1 . . . . . . . 8
1110imbi2d 309 . . . . . . 7
129, 11ceqsalv 2983 . . . . . 6
138, 12bitri 242 . . . . 5
14132albii 1577 . . . 4
156, 14bitri 242 . . 3
165, 15bitri 242 . 2
17 df-ral 2711 . 2
18 r2al 2743 . 2
1916, 17, 183bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1726  wral 2706  csn 3815  cop 3818  ciun 4094   cxp 4877 This theorem is referenced by:  rexiunxp  5016  ralxp  5017  fmpt2x  6418  ovmptss  6429  filnetlem4  26411 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-csb 3253  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-iun 4096  df-opab 4268  df-xp 4885  df-rel 4886
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