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Theorem reuxfrd 4677
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . Use reuhypd 4679 to eliminate the second hypothesis. (Contributed by NM, 16-Jan-2012.)
Hypotheses
Ref Expression
reuxfrd.1
reuxfrd.2
reuxfrd.3
Assertion
Ref Expression
reuxfrd
Distinct variable groups:   ,,   ,   ,   ,   ,,

Proof of Theorem reuxfrd
StepHypRef Expression
1 reuxfrd.2 . . . . . 6
2 reurex 3074 . . . . . 6
31, 2syl 16 . . . . 5
43biantrurd 508 . . . 4
5 r19.41v 3009 . . . . 5
6 reuxfrd.3 . . . . . . 7
76pm5.32i 637 . . . . . 6
87rexbii 2959 . . . . 5
95, 8bitr3i 251 . . . 4
104, 9syl6bb 261 . . 3
1110reubidva 3041 . 2
12 reuxfrd.1 . . 3
13 reurmo 3075 . . . 4
141, 13syl 16 . . 3
1512, 14reuxfr2d 4675 . 2
1611, 15bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E.wrex 2808  E!wreu 2809  E*wrmo 2810 This theorem is referenced by:  reuxfr  4678  riotaxfrd  6288 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  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-v 3111
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