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Theorem euxfr2 3111
 Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 14-Nov-2004.)
Hypotheses
Ref Expression
euxfr2.1
euxfr2.2
Assertion
Ref Expression
euxfr2
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem euxfr2
StepHypRef Expression
1 2euswap 2356 . . . 4
2 euxfr2.2 . . . . . 6
32moani 2332 . . . . 5
4 ancom 438 . . . . . 6
54mobii 2316 . . . . 5
63, 5mpbi 200 . . . 4
71, 6mpg 1557 . . 3
8 2euswap 2356 . . . 4
9 moeq 3102 . . . . . 6
109moani 2332 . . . . 5
114mobii 2316 . . . . 5
1210, 11mpbi 200 . . . 4
138, 12mpg 1557 . . 3
147, 13impbii 181 . 2
15 euxfr2.1 . . . 4
16 biidd 229 . . . 4
1715, 16ceqsexv 2983 . . 3
1817eubii 2289 . 2
1914, 18bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  weu 2280  wmo 2281  cvv 2948 This theorem is referenced by:  euxfr  3112  euop2  4448 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 2416 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-v 2950
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