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Theorem 3reeanv 2878
 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 2863 . . 3
2 reeanv 2877 . . . 4
32anbi1i 678 . . 3
41, 3bitri 242 . 2
5 df-3an 939 . . . . 5
652rexbii 2734 . . . 4
7 reeanv 2877 . . . 4
86, 7bitri 242 . . 3
98rexbii 2732 . 2
10 df-3an 939 . 2
114, 9, 103bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   w3a 937  wrex 2708 This theorem is referenced by:  imasmnd2  14734  imasgrp2  14935  imasrng  15727  axeuclid  25904  lshpkrlem6  29975 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713
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