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Theorem euxfr 3289
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.)
Hypotheses
Ref Expression
euxfr.1
euxfr.2
euxfr.3
Assertion
Ref Expression
euxfr
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem euxfr
StepHypRef Expression
1 euxfr.2 . . . . . 6
2 euex 2303 . . . . . 6
31, 2ax-mp 5 . . . . 5
43biantrur 506 . . . 4
5 19.41v 1945 . . . 4
6 euxfr.3 . . . . . 6
76pm5.32i 637 . . . . 5
87exbii 1644 . . . 4
94, 5, 83bitr2i 273 . . 3
109eubii 2300 . 2
11 euxfr.1 . . 3
121eumoi 2309 . . 3
1311, 12euxfr2 3288 . 2
1410, 13bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379  wex 1596   wcel 1767  weu 2275  cvv 3113 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  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-v 3115 This theorem is referenced by:  moxfr  30228
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