Theorem bj-funidres 37136

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

TODO: relabel funi 6556 to funid.

Assertion

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

Proof of Theorem bj-funidres

Step	Hyp	Ref	Expression
1		funi 6556	. 2 ⊢ Fun I
2		funres 6566	. 2 ⊢ (Fun I → Fun ( I ↾ 𝑉))
3	1, 2	ax-mp 5	1 ⊢ Fun ( I ↾ 𝑉)

Syntax hints:   I cid 5540   ↾ cres 5648  Fun wfun 6513

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-sep 5259  ax-nul 5269  ax-pr 5395

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-ral 3047  df-rex 3056  df-rab 3412  df-v 3457  df-dif 3925  df-un 3927  df-in 3929  df-ss 3939  df-nul 4305  df-if 4497  df-sn 4598  df-pr 4600  df-op 4604  df-br 5116  df-opab 5178  df-id 5541  df-xp 5652  df-rel 5653  df-cnv 5654  df-co 5655  df-res 5658  df-fun 6521

This theorem is referenced by: (None)