Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  2ralor Unicode version

Theorem 2ralor 2722
 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 2567 . . . 4
2 rexnal 2567 . . . 4
31, 2anbi12i 678 . . 3
4 ioran 476 . . . . . . 7
54rexbii 2581 . . . . . 6
6 rexnal 2567 . . . . . 6
75, 6bitr3i 242 . . . . 5
87rexbii 2581 . . . 4
9 reeanv 2720 . . . 4
10 rexnal 2567 . . . 4
118, 9, 103bitr3ri 267 . . 3
12 ioran 476 . . 3
133, 11, 123bitr4i 268 . 2
1413con4bii 288 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 176   wo 357   wa 358  wral 2556  wrex 2557 This theorem is referenced by:  2ralorOLD  26443  ispridl2  26766 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562
 Copyright terms: Public domain W3C validator