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Theorem funoprab 6162
 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 1556 . 2
3 funoprabg 6161 . 2
42, 3ax-mp 8 1
 Colors of variables: wff set class Syntax hints:  wal 1549  wmo 2281   wfun 5440  coprab 6074 This theorem is referenced by:  mpt2fun  6164  oprabex  6179  ovidig  6183  ovigg  6186  th3qcor  7004  axaddf  9012  axmulf  9013  funtransport  25957  funray  26066  funline  26068 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-fun 5448  df-oprab 6077
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