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Theorem 3reeanv 2721
 Description: Rearrange three existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.)
Assertion
Ref Expression
3reeanv
Distinct variable groups:   ,,   ,,   ,,   ,   ,,   ,,
Allowed substitution hints:   ()   ()   ()   (,)   ()   ()

Proof of Theorem 3reeanv
StepHypRef Expression
1 r19.41v 2706 . . 3
2 reeanv 2720 . . . 4
32anbi1i 676 . . 3
41, 3bitri 240 . 2
5 df-3an 936 . . . . 5
652rexbii 2583 . . . 4
7 reeanv 2720 . . . 4
86, 7bitri 240 . . 3
98rexbii 2581 . 2
10 df-3an 936 . 2
114, 9, 103bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358   w3a 934  wrex 2557 This theorem is referenced by:  imasmnd2  14425  imasgrp2  14626  imasrng  15418  axeuclid  24663  3reeanvOLD  26449  lshpkrlem6  29927 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-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562
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