Theorem bj-evalfun 37249

Description: The evaluation at a class is a function. (Contributed by BJ, 27-Dec-2021.)

Assertion

Ref	Expression
bj-evalfun	⊢ Fun Slot 𝐴

Proof of Theorem bj-evalfun

Dummy variable 𝑓 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-slot 17113	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
2	1	funmpt2 6532	1 ⊢ Fun Slot 𝐴

Syntax hints:  Vcvv 3441  Fun wfun 6487  ‘cfv 6493  Slot cslot 17112

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709  ax-sep 5242  ax-nul 5252  ax-pr 5378

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-nf 1786  df-sb 2069  df-mo 2540  df-eu 2570  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-ral 3053  df-rex 3062  df-rab 3401  df-v 3443  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4287  df-if 4481  df-sn 4582  df-pr 4584  df-op 4588  df-br 5100  df-opab 5162  df-mpt 5181  df-id 5520  df-xp 5631  df-rel 5632  df-cnv 5633  df-co 5634  df-fun 6495  df-slot 17113

This theorem is referenced by: (None)