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Theorem ralpr 3818
 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 3814 . 2
61, 2, 5mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1649   wcel 1721  wral 2663  cvv 2913  cpr 3772 This theorem is referenced by:  fzprval  11051  xpsfrnel  13729  xpsle  13747  isdrs2  14337  iblcnlem1  19618  wlkntrllem4  21488  wlkntrllem5  21489  constr2trl  21518  subfacp1lem3  24790  fprb  25312  2wlklem  27947  usgra2pthspth  27957  usgra2wlkspthlem1  27958 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-ral 2668  df-v 2915  df-sbc 3119  df-un 3282  df-sn 3777  df-pr 3778
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