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Theorem rexprg 3850
 Description: Convert a quantification over a pair to a disjunction. (Contributed by NM, 17-Sep-2011.) (Revised by Mario Carneiro, 23-Apr-2015.)
Hypotheses
Ref Expression
ralprg.1
ralprg.2
Assertion
Ref Expression
rexprg
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rexprg
StepHypRef Expression
1 df-pr 3813 . . . 4
21rexeqi 2901 . . 3
3 rexun 3519 . . 3
42, 3bitri 241 . 2
5 ralprg.1 . . . . 5
65rexsng 3839 . . . 4
76orbi1d 684 . . 3
8 ralprg.2 . . . . 5
98rexsng 3839 . . . 4
109orbi2d 683 . . 3
117, 10sylan9bb 681 . 2
124, 11syl5bb 249 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wo 358   wa 359   wceq 1652   wcel 1725  wrex 2698   cun 3310  csn 3806  cpr 3807 This theorem is referenced by:  rextpg  3852  rexpr  3854  fr2nr  4552  nb3graprlem2  21453  frgra2v  28326  3vfriswmgralem  28331 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-sbc 3154  df-un 3317  df-sn 3812  df-pr 3813
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