Theorem bj-evalfn 34929

Description: The evaluation at a class is a function on the universal class. (General form of slotfn 16684). (Contributed by Mario Carneiro, 22-Sep-2015.) (Revised by BJ, 27-Dec-2021.)

Assertion

Ref	Expression
bj-evalfn	⊢ Slot 𝐴 Fn V

Proof of Theorem bj-evalfn

Dummy variable 𝑓 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		fvex 6708	. 2 ⊢ (𝑓‘𝐴) ∈ V
2		df-slot 16670	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
3	1, 2	fnmpti 6499	1 ⊢ Slot 𝐴 Fn V

Syntax hints:  Vcvv 3398   Fn wfn 6353  ‘cfv 6358  Slot cslot 16665

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 2018  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2160  ax-12 2177  ax-ext 2708  ax-sep 5177  ax-nul 5184  ax-pr 5307

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-nf 1792  df-sb 2073  df-mo 2539  df-eu 2568  df-clab 2715  df-cleq 2728  df-clel 2809  df-nfc 2879  df-ral 3056  df-rex 3057  df-rab 3060  df-v 3400  df-sbc 3684  df-dif 3856  df-un 3858  df-in 3860  df-ss 3870  df-nul 4224  df-if 4426  df-sn 4528  df-pr 4530  df-op 4534  df-uni 4806  df-br 5040  df-opab 5102  df-mpt 5121  df-id 5440  df-xp 5542  df-rel 5543  df-cnv 5544  df-co 5545  df-dm 5546  df-iota 6316  df-fun 6360  df-fn 6361  df-fv 6366  df-slot 16670

This theorem is referenced by: (None)