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Theorem 3reeanv 2779
 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 2764 . . 3
2 reeanv 2778 . . . 4
32anbi1i 676 . . 3
41, 3bitri 240 . 2
5 df-3an 936 . . . . 5
652rexbii 2641 . . . 4
7 reeanv 2778 . . . 4
86, 7bitri 240 . . 3
98rexbii 2639 . 2
10 df-3an 936 . 2
114, 9, 103bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358   w3a 934  wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620 This theorem is referenced by:  xpassen  6057
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