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Theorem funoprab 5601
 Description: "At most one" is a sufficient condition for an operation class abstraction to be a function. (Contributed by NM, 17-Mar-1995.)
Hypothesis
Ref Expression
funoprab.1
Assertion
Ref Expression
funoprab
Distinct variable group:   ,,
Allowed substitution hints:   (,,)

Proof of Theorem funoprab
StepHypRef Expression
1 funoprab.1 . . 3
21gen2 1339 . 2
3 funoprabg 5600 . 2
42, 3ax-mp 7 1
 Colors of variables: wff set class Syntax hints:  wal 1241  wmo 1901   wfun 4896  coprab 5513 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-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-fun 4904  df-oprab 5516 This theorem is referenced by:  mpt2fun  5603  ovidig  5618  ovigg  5621  oprabex  5755  th3qcor  6210
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