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Theorem fnmpti 5246
 Description: Functionality and domain of an ordered-pair class abstraction. (Contributed by NM, 29-Jan-2004.) (Revised by Mario Carneiro, 31-Aug-2015.)
Hypotheses
Ref Expression
fnmpti.1
fnmpti.2
Assertion
Ref Expression
fnmpti
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem fnmpti
StepHypRef Expression
1 fnmpti.1 . . 3
21rgenw 2485 . 2
3 fnmpti.2 . . 3
43mptfng 5243 . 2
52, 4mpbi 144 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wcel 1480  wral 2414  cvv 2681   cmpt 3984   wfn 5113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-mpt 3986  df-id 4210  df-xp 4540  df-rel 4541  df-cnv 4542  df-co 4543  df-dm 4544  df-fun 5120  df-fn 5121 This theorem is referenced by:  dmmpti  5247  fconst  5313  eufnfv  5641  idref  5651  fo1st  6048  fo2nd  6049  reldm  6077  oafnex  6333  fnoei  6341  oeiexg  6342  mapsnf1o2  6583  slotslfn  11974  topnfn  12114  fncld  12256  xmetunirn  12516
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