Theorem bj-evalfun 36410

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 17111	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
2	1	funmpt2 6577	1 ⊢ Fun Slot 𝐴

Syntax hints:  Vcvv 3466  Fun wfun 6527  ‘cfv 6533  Slot cslot 17110

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-sep 5289  ax-nul 5296  ax-pr 5417

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-eu 2555  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-br 5139  df-opab 5201  df-mpt 5222  df-id 5564  df-xp 5672  df-rel 5673  df-cnv 5674  df-co 5675  df-fun 6535  df-slot 17111

This theorem is referenced by: (None)