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Theorem rexpr 4057
 Description: Convert an existential quantification over a pair to a disjunction. (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
rexpr
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rexpr
StepHypRef Expression
1 ralpr.1 . 2
2 ralpr.2 . 2
3 ralpr.3 . . 3
4 ralpr.4 . . 3
53, 4rexprg 4053 . 2
61, 2, 5mp2an 676 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wo 369   wceq 1437   wcel 1870  wrex 2783  cvv 3087  cpr 4004 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rex 2788  df-v 3089  df-sbc 3306  df-un 3447  df-sn 4003  df-pr 4005 This theorem is referenced by:  xpsdsval  21327  poimir  31680
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