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Theorem eu2 1944
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 1930 . . 3
2 eu2.1 . . . . . 6  F/
32nfri 1412 . . . . 5
43eumo0 1931 . . . 4
52mo23 1941 . . . 4
64, 5syl 14 . . 3
71, 6jca 290 . 2
8 19.29r 1512 . . . 4
9 impexp 250 . . . . . . . . 9
109albii 1359 . . . . . . . 8
11219.21 1475 . . . . . . . 8
1210, 11bitri 173 . . . . . . 7
1312anbi2i 430 . . . . . 6
14 abai 494 . . . . . 6
1513, 14bitr4i 176 . . . . 5
1615exbii 1496 . . . 4
178, 16sylib 127 . . 3
183eu1 1925 . . 3
1917, 18sylibr 137 . 2
207, 19impbii 117 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1241   F/wnf 1349  wex 1381  wsb 1645  weu 1900
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903
This theorem is referenced by:  eu3h  1945  mo3h  1953  bm1.1  2025  reu2  2726
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