Theorem bj-evalfun 34358

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 16481	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
2	1	funmpt2 6388	1 ⊢ Fun Slot 𝐴

Syntax hints:  Vcvv 3494  Fun wfun 6343  ‘cfv 6349  Slot cslot 16476

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 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793  ax-sep 5195  ax-nul 5202  ax-pr 5321

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-mo 2618  df-eu 2650  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ral 3143  df-rab 3147  df-v 3496  df-dif 3938  df-un 3940  df-in 3942  df-ss 3951  df-nul 4291  df-if 4467  df-sn 4561  df-pr 4563  df-op 4567  df-br 5059  df-opab 5121  df-mpt 5139  df-id 5454  df-xp 5555  df-rel 5556  df-cnv 5557  df-co 5558  df-fun 6351  df-slot 16481

This theorem is referenced by:  bj-isrvec  34569