Theorem bj-funidres 36499

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

Step	Hyp	Ref	Expression
1		funi 6580	. 2 ⊢ Fun I
2		funres 6590	. 2 ⊢ (Fun I → Fun ( I ↾ 𝑉))
3	1, 2	ax-mp 5	1 ⊢ Fun ( I ↾ 𝑉)

Syntax hints:   I cid 5573   ↾ cres 5678  Fun wfun 6537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702  ax-sep 5299  ax-nul 5306  ax-pr 5427

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-ral 3061  df-rex 3070  df-rab 3432  df-v 3475  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-res 5688  df-fun 6545

This theorem is referenced by: (None)