ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  funmpt2 Structured version   GIF version

Theorem funmpt2 4882
Description: Functionality of a class given by a "maps to" notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.)
Hypothesis
Ref Expression
funmpt2.1 𝐹 = (x AB)
Assertion
Ref Expression
funmpt2 Fun 𝐹

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 4881 . 2 Fun (x AB)
2 funmpt2.1 . . 3 𝐹 = (x AB)
32funeqi 4865 . 2 (Fun 𝐹 ↔ Fun (x AB))
41, 3mpbir 134 1 Fun 𝐹
Colors of variables: wff set class
Syntax hints:   = wceq 1242  cmpt 3809  Fun wfun 4839
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-mpt 3811  df-id 4021  df-xp 4294  df-rel 4295  df-cnv 4296  df-co 4297  df-fun 4847
This theorem is referenced by:  fvmptss2  5190  frectfr  5924
  Copyright terms: Public domain W3C validator