Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  fnmpti Unicode version

Theorem fnmpti 5027
 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 2376 . 2
3 fnmpti.2 . . 3
43mptfng 5024 . 2
52, 4mpbi 133 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  wral 2306  cvv 2557   cmpt 3818   wfn 4897 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-mpt 3820  df-id 4030  df-xp 4351  df-rel 4352  df-cnv 4353  df-co 4354  df-dm 4355  df-fun 4904  df-fn 4905 This theorem is referenced by:  dmmpti  5028  fconst  5082  eufnfv  5389  idref  5396  fo1st  5784  fo2nd  5785  reldm  5812  oafnex  6024  fnoei  6032  oeiexg  6033
 Copyright terms: Public domain W3C validator