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Theorem funoprab 6402
 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:   ,,

Proof of Theorem funoprab
StepHypRef Expression
1 funoprab.1 . . 3
21gen2 1619 . 2
3 funoprabg 6401 . 2
42, 3ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  A.wal 1393  E*wmo 2283  Funwfun 5587  {coprab 6297 This theorem is referenced by:  mpt2fun  6404  ovidig  6420  ovigg  6423  oprabex  6788  axaddf  9543  axmulf  9544  funtransport  29681  funray  29790  funline  29792 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-fun 5595  df-oprab 6300
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