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Theorem euxfr2 3288
 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 2379 . . . 4
2 euxfr2.2 . . . . . 6
32moani 2348 . . . . 5
4 ancom 450 . . . . . 6
54mobii 2301 . . . . 5
63, 5mpbi 208 . . . 4
71, 6mpg 1603 . . 3
8 2euswap 2379 . . . 4
9 moeq 3279 . . . . . 6
109moani 2348 . . . . 5
114mobii 2301 . . . . 5
1210, 11mpbi 208 . . . 4
138, 12mpg 1603 . . 3
147, 13impbii 188 . 2
15 euxfr2.1 . . . 4
16 biidd 237 . . . 4
1715, 16ceqsexv 3150 . . 3
1817eubii 2300 . 2
1914, 18bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379  wex 1596   wcel 1767  weu 2275  wmo 2276  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:  euxfr  3289  euop2  4747
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