Theorem bj-funidres 37132

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

TODO: relabel funi 6532 to funid.

Assertion

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

Proof of Theorem bj-funidres

Step	Hyp	Ref	Expression
1		funi 6532	. 2 ⊢ Fun I
2		funres 6542	. 2 ⊢ (Fun I → Fun ( I ↾ 𝑉))
3	1, 2	ax-mp 5	1 ⊢ Fun ( I ↾ 𝑉)

Syntax hints:   I cid 5525   ↾ cres 5633  Fun wfun 6493

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 2701  ax-sep 5246  ax-nul 5256  ax-pr 5382

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 2708  df-cleq 2721  df-clel 2803  df-ral 3045  df-rex 3054  df-rab 3403  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4293  df-if 4485  df-sn 4586  df-pr 4588  df-op 4592  df-br 5103  df-opab 5165  df-id 5526  df-xp 5637  df-rel 5638  df-cnv 5639  df-co 5640  df-res 5643  df-fun 6501

This theorem is referenced by: (None)