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Theorem euxfr 3022
 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 2227 . . . . . 6
31, 2ax-mp 5 . . . . 5
43biantrur 492 . . . 4
5 19.41v 1901 . . . 4
6 euxfr.3 . . . . . 6
76pm5.32i 618 . . . . 5
87exbii 1582 . . . 4
94, 5, 83bitr2i 264 . . 3
109eubii 2213 . 2
11 euxfr.1 . . 3
121eumoi 2245 . . 3
1311, 12euxfr2 3021 . 2
1410, 13bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  weu 2204  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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