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Theorem 3reeanv 3035
 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 3019 . . 3
2 reeanv 3034 . . . 4
32anbi1i 695 . . 3
41, 3bitri 249 . 2
5 df-3an 975 . . . . 5
652rexbii 2970 . . . 4
7 reeanv 3034 . . . 4
86, 7bitri 249 . . 3
98rexbii 2969 . 2
10 df-3an 975 . 2
114, 9, 103bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   w3a 973  wrex 2818 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1597  df-nf 1600  df-ral 2822  df-rex 2823 This theorem is referenced by:  imasmnd2  15830  imasgrp2  16057  imasring  17140  axeuclid  24089  lshpkrlem6  34313
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