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Theorem 2ralor 2780
 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 2625 . . . 4
2 rexnal 2625 . . . 4
31, 2anbi12i 678 . . 3
4 ioran 476 . . . . . . 7
54rexbii 2639 . . . . . 6
6 rexnal 2625 . . . . . 6
75, 6bitr3i 242 . . . . 5
87rexbii 2639 . . . 4
9 reeanv 2778 . . . 4
10 rexnal 2625 . . . 4
118, 9, 103bitr3ri 267 . . 3
12 ioran 476 . . 3
133, 11, 123bitr4i 268 . 2
1413con4bii 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176   wo 357   wa 358  wral 2614  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620 This theorem is referenced by: (None)
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