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Theorem funoprabg 6172
 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 4457 . . 3
21alrimiv 1642 . 2
3 dfoprab2 6124 . . . 4
43funeqi 5477 . . 3
5 funopab 5489 . . 3
64, 5bitr2i 243 . 2
72, 6sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550  wex 1551   wceq 1653  wmo 2284  cop 3819  copab 4268   wfun 5451  coprab 6085 This theorem is referenced by:  funoprab  6173  fnoprabg  6174  oprabexd  6189 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-fun 5459  df-oprab 6088
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