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Theorem ralpr 3861
 Description: Convert a quantification over a pair to a conjunction. (Contributed by NM, 3-Jun-2007.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypotheses
Ref Expression
ralpr.1
ralpr.2
ralpr.3
ralpr.4
Assertion
Ref Expression
ralpr
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ralpr
StepHypRef Expression
1 ralpr.1 . 2
2 ralpr.2 . 2
3 ralpr.3 . . 3
4 ralpr.4 . . 3
53, 4ralprg 3857 . 2
61, 2, 5mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2705  cvv 2956  cpr 3815 This theorem is referenced by:  fzprval  11106  xpsfrnel  13788  xpsle  13806  isdrs2  14396  iblcnlem1  19679  wlkntrllem2  21560  wlkntrllem3  21561  2wlklem  21564  subfacp1lem3  24868  fprb  25397  usgra2pthspth  28305  usgra2wlkspthlem1  28306 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-sbc 3162  df-un 3325  df-sn 3820  df-pr 3821
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