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Theorem funopab 5478
 Description: A class of ordered pairs is a function when there is at most one second member for each pair. (Contributed by NM, 16-May-1995.)
Assertion
Ref Expression
funopab
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem funopab
StepHypRef Expression
1 relopab 4993 . . 3
2 nfopab1 4266 . . . 4
3 nfopab2 4267 . . . 4
42, 3dffun6f 5460 . . 3
51, 4mpbiran 885 . 2
6 df-br 4205 . . . . 5
7 opabid 4453 . . . . 5
86, 7bitri 241 . . . 4
98mobii 2316 . . 3
109albii 1575 . 2
115, 10bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549   wcel 1725  wmo 2281  cop 3809   class class class wbr 4204  copab 4257   wrel 4875   wfun 5440 This theorem is referenced by:  funopabeq  5479  funco  5483  isarep2  5525  fnopabg  5560  fvopab3ig  5795  opabex  5956  zfrep6  5960  funoprabg  6161  opabiotafun  6528  tz7.44lem1  6655  ajfuni  22351  funadj  23379  abrexdomjm  23978  mptfnf  24063  abrexdom  26386 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
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