Theorem bj-evalfun 37056

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 17216	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
2	1	funmpt2 6607	1 ⊢ Fun Slot 𝐴

Syntax hints:  Vcvv 3478  Fun wfun 6557  ‘cfv 6563  Slot cslot 17215

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149  df-opab 5211  df-mpt 5232  df-id 5583  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-fun 6565  df-slot 17216

This theorem is referenced by: (None)