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Theorem rexpr 3780
 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 3776 . 2
61, 2, 5mp2an 653 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wo 357   wceq 1642   wcel 1710  wrex 2615  cvv 2859  cpr 3738 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742 This theorem is referenced by: (None)
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