Theorem bj-evalfn 37511

Description: The evaluation at a class is a function on the universal class. (General form of slotfn 17196). (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 6869	. 2 ⊢ (𝑓‘𝐴) ∈ V
2		df-slot 17194	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
3	1, 2	fnmpti 6653	1 ⊢ Slot 𝐴 Fn V

Syntax hints:  Vcvv 3448   Fn wfn 6505  ‘cfv 6510  Slot cslot 17193

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-10 2169  ax-11 2185  ax-12 2206  ax-ext 2728  ax-sep 5240  ax-nul 5250  ax-pr 5384

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-3an 1097  df-tru 1557  df-fal 1567  df-ex 1794  df-nf 1798  df-sb 2085  df-mo 2560  df-eu 2590  df-clab 2735  df-cleq 2748  df-clel 2831  df-nfc 2905  df-ne 2952  df-ral 3071  df-rex 3081  df-rab 3409  df-v 3450  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4281  df-if 4475  df-sn 4577  df-pr 4579  df-op 4583  df-uni 4860  df-br 5095  df-opab 5157  df-mpt 5176  df-id 5535  df-xp 5646  df-rel 5647  df-cnv 5648  df-co 5649  df-dm 5650  df-iota 6466  df-fun 6512  df-fn 6513  df-fv 6518  df-slot 17194

This theorem is referenced by: (None)