Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-funidres Structured version   Visualization version   GIF version

Theorem bj-funidres 36683
Description: The restricted identity relation is a function. (Contributed by BJ, 27-Dec-2023.)

TODO: relabel funi 6580 to funid.

Assertion
Ref Expression
bj-funidres Fun ( I ↾ 𝑉)

Proof of Theorem bj-funidres
StepHypRef Expression
1 funi 6580 . 2 Fun I
2 funres 6590 . 2 (Fun I → Fun ( I ↾ 𝑉))
31, 2ax-mp 5 1 Fun ( I ↾ 𝑉)
Colors of variables: wff setvar class
Syntax hints:   I cid 5570  cres 5675  Fun wfun 6537
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696  ax-sep 5295  ax-nul 5302  ax-pr 5424
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3465  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4320  df-if 4526  df-sn 4626  df-pr 4628  df-op 4632  df-br 5145  df-opab 5207  df-id 5571  df-xp 5679  df-rel 5680  df-cnv 5681  df-co 5682  df-res 5685  df-fun 6545
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator