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Theorem ralxp 5008
 Description: Universal quantification restricted to a cross product is equivalent to a double restricted quantification. The hypothesis specifies an implicit substitution. (Contributed by NM, 7-Feb-2004.) (Revised by Mario Carneiro, 29-Dec-2014.)
Hypothesis
Ref Expression
ralxp.1
Assertion
Ref Expression
ralxp
Distinct variable groups:   ,,,   ,,   ,,   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem ralxp
StepHypRef Expression
1 iunxpconst 4926 . . 3
21raleqi 2900 . 2
3 ralxp.1 . . 3
43raliunxp 5006 . 2
52, 4bitr3i 243 1
 Colors of variables: wff set class Syntax hints:  ->wi 4  <->wb 177  =wceq 1652  A.wral 2697  {csn 3806  <.cop 3809  U_ciun 4085  X.cxp 4868 This theorem is referenced by:  ralxpf  5011  issref  5239  ffnov  6166  eqfnov  6168  funimassov  6215  f1stres  6360  f2ndres  6361  ecopover  7000  xpf1o  7261  xpwdomg  7545  rankxplim  7795  imasaddfnlem  13745  imasvscafn  13754  comfeq  13924  isssc  14012  isfuncd  14054  cofucl  14077  funcres2b  14086  evlfcl  14311  uncfcurf  14328  yonedalem3  14369  yonedainv  14370  efgval2  15348  txbas  17591  hausdiag  17669  tx1stc  17674  txkgen  17676  xkococn  17684  cnmpt21  17695  xkoinjcn  17711  tmdcn2  18111  clssubg  18130  divstgplem  18142  txmetcnp  18569  txmetcn  18570  qtopbaslem  18784  bndth  18975  cxpcn3  20624  dvdsmulf1o  20971  fsumdvdsmul  20972  xrofsup  24118  txpcon  24911  cvmlift2lem1  24981  cvmlift2lem12  24993  f1opr  26417  ismtyhmeolem  26504  ffnaov  28030  dih1dimatlem  32064 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-iun 4087  df-opab 4259  df-xp 4876  df-rel 4877
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