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Theorem euxfr2 3021
 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 2280 . . . 4
2 euxfr2.2 . . . . . 6
32moani 2256 . . . . 5
4 ancom 437 . . . . . 6
54mobii 2240 . . . . 5
63, 5mpbi 199 . . . 4
71, 6mpg 1548 . . 3
8 2euswap 2280 . . . 4
9 moeq 3012 . . . . . 6
109moani 2256 . . . . 5
114mobii 2240 . . . . 5
1210, 11mpbi 199 . . . 4
138, 12mpg 1548 . . 3
147, 13impbii 180 . 2
15 euxfr2.1 . . . 4
16 biidd 228 . . . 4
1715, 16ceqsexv 2894 . . 3
1817eubii 2213 . 2
1914, 18bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541   wceq 1642   wcel 1710  weu 2204  wmo 2205  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:  euxfr  3022
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