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Theorem bj-evalfun 33349
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.
StepHypRef Expression
1 df-slot 16083 . 2 Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓𝐴))
21funmpt2 6088 1 Fun Slot 𝐴
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3340  Fun wfun 6043  cfv 6049  Slot cslot 16078
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pr 5055
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-sn 4322  df-pr 4324  df-op 4328  df-br 4805  df-opab 4865  df-mpt 4882  df-id 5174  df-xp 5272  df-rel 5273  df-cnv 5274  df-co 5275  df-fun 6051  df-slot 16083
This theorem is referenced by: (None)
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