Theorem bj-funidres 37823

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

TODO: relabel funi 6568 to funid.

Assertion

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

Proof of Theorem bj-funidres

Step	Hyp	Ref	Expression
1		funi 6568	. 2 ⊢ Fun I
2		funres 6578	. 2 ⊢ (Fun I → Fun ( I ↾ 𝑉))
3	1, 2	ax-mp 5	1 ⊢ Fun ( I ↾ 𝑉)

This proof depends on syntax axioms:   I cid 5554   ↾ cres 5662  Fun wfun 6530

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-9 2152  ax-ext 2734  ax-sep 5256  ax-pr 5403

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1104  df-tru 1572  df-fal 1582  df-ex 1809  df-sb 2096  df-clab 2741  df-cleq 2754  df-clel 2837  df-ral 3079  df-rex 3089  df-rab 3416  df-v 3456  df-dif 3907  df-un 3909  df-in 3911  df-ss 3921  df-nul 4286  df-if 4487  df-sn 4589  df-pr 4591  df-op 4595  df-br 5109  df-opab 5173  df-id 5555  df-xp 5666  df-rel 5667  df-cnv 5668  df-co 5669  df-res 5672  df-fun 6538

This theorem is used by: (None)