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Theorem funoprabg 5652
 Description: "At most one" is a sufficient condition for an operation class abstraction to be a function. (Contributed by NM, 28-Aug-2007.)
Assertion
Ref Expression
funoprabg
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem funoprabg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mosubopt 4451 . . 3
21alrimiv 1797 . 2
3 dfoprab2 5604 . . . 4
43funeqi 4972 . . 3
5 funopab 4985 . . 3
64, 5bitr2i 183 . 2
72, 6sylib 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102  wal 1283   wceq 1285  wex 1422  wmo 1944  cop 3419  copab 3858   wfun 4946  coprab 5565 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-pow 3968  ax-pr 3992 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pw 3402  df-sn 3422  df-pr 3423  df-op 3425  df-br 3806  df-opab 3860  df-id 4076  df-xp 4397  df-rel 4398  df-cnv 4399  df-co 4400  df-fun 4954  df-oprab 5568 This theorem is referenced by:  funoprab  5653  fnoprabg  5654  oprabexd  5806
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