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Theorem rexiunxp 5018
 Description: Write a double restricted quantification as one universal quantifier. In this version of rexxp 5020, is not assumed to be constant. (Contributed by Mario Carneiro, 14-Feb-2015.)
Hypothesis
Ref Expression
ralxp.1
Assertion
Ref Expression
rexiunxp
Distinct variable groups:   ,,,   ,,   ,,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem rexiunxp
StepHypRef Expression
1 ralxp.1 . . . . . 6
21notbid 287 . . . . 5
32raliunxp 5017 . . . 4
4 ralnex 2717 . . . . 5
54ralbii 2731 . . . 4
63, 5bitri 242 . . 3
76notbii 289 . 2
8 dfrex2 2720 . 2
9 dfrex2 2720 . 2
107, 8, 93bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wceq 1653  wral 2707  wrex 2708  csn 3816  cop 3819  ciun 4095   cxp 4879 This theorem is referenced by:  rexxp  5020  fsumvma  21002  cvmliftlem15  24990  filnetlem4  26424 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 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 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-iun 4097  df-opab 4270  df-xp 4887  df-rel 4888
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