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Theorem fnresiOLD 6453
 Description: Obsolete proof of fnresi 6452 as of 27-Dec-2023. (Contributed by NM, 27-Aug-2004.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
fnresiOLD ( I ↾ 𝐴) Fn 𝐴

Proof of Theorem fnresiOLD
StepHypRef Expression
1 funi 6360 . . 3 Fun I
2 funres 6370 . . 3 (Fun I → Fun ( I ↾ 𝐴))
31, 2ax-mp 5 . 2 Fun ( I ↾ 𝐴)
4 dmresi 5892 . 2 dom ( I ↾ 𝐴) = 𝐴
5 df-fn 6331 . 2 (( I ↾ 𝐴) Fn 𝐴 ↔ (Fun ( I ↾ 𝐴) ∧ dom ( I ↾ 𝐴) = 𝐴))
63, 4, 5mpbir2an 710 1 ( I ↾ 𝐴) Fn 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   I cid 5427  dom cdm 5523   ↾ cres 5525  Fun wfun 6322   Fn wfn 6323 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773  ax-sep 5170  ax-nul 5177  ax-pr 5298 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-mo 2601  df-eu 2632  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-ral 3114  df-rex 3115  df-v 3446  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4247  df-if 4429  df-sn 4529  df-pr 4531  df-op 4535  df-br 5034  df-opab 5096  df-id 5428  df-xp 5529  df-rel 5530  df-cnv 5531  df-co 5532  df-dm 5533  df-res 5535  df-fun 6330  df-fn 6331 This theorem is referenced by: (None)
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