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Theorem mo23 2038
 Description: An implication between two definitions of "there exists at most one." (Contributed by Jim Kingdon, 25-Jun-2018.)
Hypothesis
Ref Expression
mo23.1
Assertion
Ref Expression
mo23
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem mo23
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mo23.1 . . . . 5
2 nfv 1508 . . . . 5
31, 2nfim 1551 . . . 4
43nfal 1555 . . 3
5 nfv 1508 . . 3
6 equequ2 1689 . . . . 5
76imbi2d 229 . . . 4
87albidv 1796 . . 3
94, 5, 8cbvex 1729 . 2
10 nfs1v 1910 . . . . . . . 8
11 nfv 1508 . . . . . . . 8
1210, 11nfim 1551 . . . . . . 7
13 sbequ2 1742 . . . . . . . 8
14 ax-8 1482 . . . . . . . 8
1513, 14imim12d 74 . . . . . . 7
163, 12, 15cbv3 1720 . . . . . 6
1716ancli 321 . . . . 5
183nfri 1499 . . . . . 6
1912nfri 1499 . . . . . 6
2018, 19aaanh 1565 . . . . 5
2117, 20sylibr 133 . . . 4
22 anim12 341 . . . . . 6
23 equtr2 1687 . . . . . 6
2422, 23syl6 33 . . . . 5
25242alimi 1432 . . . 4
2621, 25syl 14 . . 3
2726exlimiv 1577 . 2
289, 27sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wal 1329  wnf 1436  wex 1468  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736 This theorem is referenced by:  modc  2040  eu2  2041  eu3h  2042
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