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Theorem 2ralor 3027
 Description: Distribute restricted universal quantification over "or". (Contributed by Jeff Madsen, 19-Jun-2010.)
Assertion
Ref Expression
2ralor
Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem 2ralor
StepHypRef Expression
1 rexnal 2905 . . . 4
2 rexnal 2905 . . . 4
31, 2anbi12i 697 . . 3
4 ioran 490 . . . . . . 7
54rexbii 2959 . . . . . 6
6 rexnal 2905 . . . . . 6
75, 6bitr3i 251 . . . . 5
87rexbii 2959 . . . 4
9 reeanv 3025 . . . 4
10 rexnal 2905 . . . 4
118, 9, 103bitr3ri 276 . . 3
12 ioran 490 . . 3
133, 11, 123bitr4i 277 . 2
1413con4bii 297 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369  A.wral 2807  E.wrex 2808 This theorem is referenced by:  ispridl2  30435 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813
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