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Theorem 2ralor 2995
 Description: Distribute restricted universal 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 2870 . . . 4
2 rexnal 2870 . . . 4
31, 2anbi12i 701 . . 3
4 ioran 492 . . . . . . 7
54rexbii 2924 . . . . . 6
6 rexnal 2870 . . . . . 6
75, 6bitr3i 254 . . . . 5
87rexbii 2924 . . . 4
9 reeanv 2993 . . . 4
10 rexnal 2870 . . . 4
118, 9, 103bitr3ri 279 . . 3
12 ioran 492 . . 3
133, 11, 123bitr4i 280 . 2
1413con4bii 298 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187   wo 369   wa 370  wral 2771  wrex 2772 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ex 1658  df-nf 1662  df-ral 2776  df-rex 2777 This theorem is referenced by:  ispridl2  32235
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