Theorem bj-funidres 35225

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

TODO: relabel funi 6447 to funid.

Assertion

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

Proof of Theorem bj-funidres

Step	Hyp	Ref	Expression
1		funi 6447	. 2 ⊢ Fun I
2		funres 6457	. 2 ⊢ (Fun I → Fun ( I ↾ 𝑉))
3	1, 2	ax-mp 5	1 ⊢ Fun ( I ↾ 𝑉)

Syntax hints:   I cid 5478   ↾ cres 5581  Fun wfun 6409

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-12 2177  ax-ext 2710  ax-sep 5216  ax-nul 5223  ax-pr 5346

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2073  df-clab 2717  df-cleq 2731  df-clel 2818  df-ral 3069  df-rex 3070  df-rab 3073  df-v 3425  df-dif 3887  df-un 3889  df-in 3891  df-ss 3901  df-nul 4255  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-br 5071  df-opab 5133  df-id 5479  df-xp 5585  df-rel 5586  df-cnv 5587  df-co 5588  df-res 5591  df-fun 6417

This theorem is referenced by: (None)