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Theorem euxfr 3120
 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 2304 . . . . . 6
31, 2ax-mp 8 . . . . 5
43biantrur 493 . . . 4
5 19.41v 1924 . . . 4
6 euxfr.3 . . . . . 6
76pm5.32i 619 . . . . 5
87exbii 1592 . . . 4
94, 5, 83bitr2i 265 . . 3
109eubii 2290 . 2
11 euxfr.1 . . 3
121eumoi 2322 . . 3
1311, 12euxfr2 3119 . 2
1410, 13bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  weu 2281  cvv 2956 This theorem is referenced by:  moxfr  26733 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958
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