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Theorem 3reeanv 3026
Description: Rearrange three restricted existential quantifiers. (Contributed by Jeff Madsen, 11-Jun-2010.)
Assertion
Ref Expression
3reeanv
Distinct variable groups:   , ,   , ,   , ,   ,   , ,   , ,

Proof of Theorem 3reeanv
StepHypRef Expression
1 r19.41v 3009 . . 3
2 reeanv 3025 . . . 4
32anbi1i 695 . . 3
41, 3bitri 249 . 2
5 df-3an 975 . . . . 5
652rexbii 2960 . . . 4
7 reeanv 3025 . . . 4
86, 7bitri 249 . . 3
98rexbii 2959 . 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  E.wrex 2808
This theorem is referenced by:  imasmnd2  15957  imasgrp2  16185  imasring  17268  axeuclid  24266  lshpkrlem6  34840
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-ral 2812  df-rex 2813
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