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Theorem raliunxp 4979
 Description: Write a double restricted quantification as one universal quantifier. In this version of ralxp 4981, 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 4977 . . . . . 6
21imbi1i 332 . . . . 5
3 19.23vv 1827 . . . . 5
42, 3bitr4i 260 . . . 4
54albii 1699 . . 3
6 alrot3 1941 . . . 4
7 impexp 453 . . . . . . 7
87albii 1699 . . . . . 6
9 opex 4664 . . . . . . 7
10 ralxp.1 . . . . . . . 8
1110imbi2d 323 . . . . . . 7
129, 11ceqsalv 3061 . . . . . 6
138, 12bitri 257 . . . . 5
14132albii 1700 . . . 4
156, 14bitri 257 . . 3
165, 15bitri 257 . 2
17 df-ral 2761 . 2
18 r2al 2783 . 2
1916, 17, 183bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  wral 2756  csn 3959  cop 3965  ciun 4269   cxp 4837 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-iun 4271  df-opab 4455  df-xp 4845  df-rel 4846 This theorem is referenced by:  rexiunxp  4980  ralxp  4981  fmpt2x  6878  ovmptss  6896  filnetlem4  31108
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