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Theorem euxfr2 3284
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:   ,   ,

Proof of Theorem euxfr2
StepHypRef Expression
1 2euswap 2370 . . . 4
2 euxfr2.2 . . . . . 6
32moani 2346 . . . . 5
4 ancom 450 . . . . . 6
54mobii 2307 . . . . 5
63, 5mpbi 208 . . . 4
71, 6mpg 1620 . . 3
8 2euswap 2370 . . . 4
9 moeq 3275 . . . . . 6
109moani 2346 . . . . 5
114mobii 2307 . . . . 5
1210, 11mpbi 208 . . . 4
138, 12mpg 1620 . . 3
147, 13impbii 188 . 2
15 euxfr2.1 . . . 4
16 biidd 237 . . . 4
1715, 16ceqsexv 3146 . . 3
1817eubii 2306 . 2
1914, 18bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  E!weu 2282  E*wmo 2283   cvv 3109
This theorem is referenced by:  euxfr  3285  euop2  4752
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111
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