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Theorem funopab 5626
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:   ,

Proof of Theorem funopab
StepHypRef Expression
1 relopab 5134 . . 3
2 nfopab1 4518 . . . 4
3 nfopab2 4519 . . . 4
42, 3dffun6f 5607 . . 3
51, 4mpbiran 918 . 2
6 df-br 4453 . . . . 5
7 opabid 4759 . . . . 5
86, 7bitri 249 . . . 4
98mobii 2307 . . 3
109albii 1640 . 2
115, 10bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1393  e.wcel 1818  E*wmo 2283  <.cop 4035   class class class wbr 4452  {copab 4509  Relwrel 5009  Funwfun 5587
This theorem is referenced by:  funopabeq  5627  funco  5631  isarep2  5673  fnopabg  5709  opabiotafun  5934  fvopab3ig  5953  opabex  6141  funoprabg  6401  zfrep6  6768  tz7.44lem1  7090  ajfuni  25775  funadj  26805  abrexdomjm  27405  mptfnf  27499  abrexdom  30221
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
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