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Theorem ralxp 5018
 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 4936 . . 3
21raleqi 2910 . 2
3 ralxp.1 . . 3
43raliunxp 5016 . 2
52, 4bitr3i 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653  wral 2707  csn 3816  cop 3819  ciun 4095   cxp 4878 This theorem is referenced by:  ralxpf  5021  issref  5249  ffnov  6176  eqfnov  6178  funimassov  6225  f1stres  6370  f2ndres  6371  ecopover  7010  xpf1o  7271  xpwdomg  7555  rankxplim  7805  imasaddfnlem  13755  imasvscafn  13764  comfeq  13934  isssc  14022  isfuncd  14064  cofucl  14087  funcres2b  14096  evlfcl  14321  uncfcurf  14338  yonedalem3  14379  yonedainv  14380  efgval2  15358  txbas  17601  hausdiag  17679  tx1stc  17684  txkgen  17686  xkococn  17694  cnmpt21  17705  xkoinjcn  17721  tmdcn2  18121  clssubg  18140  divstgplem  18152  txmetcnp  18579  txmetcn  18580  qtopbaslem  18794  bndth  18985  cxpcn3  20634  dvdsmulf1o  20981  fsumdvdsmul  20982  xrofsup  24128  txpcon  24921  cvmlift2lem1  24991  cvmlift2lem12  25003  f1opr  26428  ismtyhmeolem  26515  ffnaov  28041  dih1dimatlem  32189 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 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 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 4269  df-xp 4886  df-rel 4887
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