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Theorem eu2 1941
Description: An alternate way of defining existential uniqueness. Definition 6.10 of [TakeutiZaring] p. 26. (Contributed by NM, 8-Jul-1994.)
Hypothesis
Ref Expression
eu2.1  F/
Assertion
Ref Expression
eu2
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem eu2
StepHypRef Expression
1 euex 1927 . . 3
2 eu2.1 . . . . . 6  F/
32nfri 1409 . . . . 5
43eumo0 1928 . . . 4
52mo23 1938 . . . 4
64, 5syl 14 . . 3
71, 6jca 290 . 2
8 19.29r 1509 . . . 4
9 impexp 250 . . . . . . . . 9
109albii 1356 . . . . . . . 8
11219.21 1472 . . . . . . . 8
1210, 11bitri 173 . . . . . . 7
1312anbi2i 430 . . . . . 6
14 abai 494 . . . . . 6
1513, 14bitr4i 176 . . . . 5
1615exbii 1493 . . . 4
178, 16sylib 127 . . 3
183eu1 1922 . . 3
1917, 18sylibr 137 . 2
207, 19impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   F/wnf 1346  wex 1378  wsb 1642  weu 1897
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900
This theorem is referenced by:  eu3h  1942  mo3h  1950  bm1.1  2022  reu2  2723
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