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Theorem 2ralor 2877
 Description: Distribute quantification over "or". (Contributed by Jeff Madsen, 19-Jun-2010.)
Assertion
Ref Expression
2ralor
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem 2ralor
StepHypRef Expression
1 rexnal 2716 . . . 4
2 rexnal 2716 . . . 4
31, 2anbi12i 679 . . 3
4 ioran 477 . . . . . . 7
54rexbii 2730 . . . . . 6
6 rexnal 2716 . . . . . 6
75, 6bitr3i 243 . . . . 5
87rexbii 2730 . . . 4
9 reeanv 2875 . . . 4
10 rexnal 2716 . . . 4
118, 9, 103bitr3ri 268 . . 3
12 ioran 477 . . 3
133, 11, 123bitr4i 269 . 2
1413con4bii 289 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wo 358   wa 359  wral 2705  wrex 2706 This theorem is referenced by:  ispridl2  26648 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-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711
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