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Theorem 3reeanv 2605
 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 2591 . . 3
2 reeanv 2604 . . . 4
32anbi1i 454 . . 3
41, 3bitri 183 . 2
5 df-3an 965 . . . . 5
652rexbii 2448 . . . 4
7 reeanv 2604 . . . 4
86, 7bitri 183 . . 3
98rexbii 2446 . 2
10 df-3an 965 . 2
114, 9, 103bitr4i 211 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   w3a 963  wrex 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423 This theorem is referenced by: (None)
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