Theorem bj-evalf 38186

Description: The evaluation at a class is a function from the universal class into the universal class. (Contributed by BJ, 17-Mar-2026.)

Assertion

Ref	Expression
bj-evalf	⊢ Slot 𝐴:V⟶V

Proof of Theorem bj-evalf

Dummy variable 𝑓 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-slot 17389	. 2 ⊢ Slot 𝐴 = (𝑓 ∈ V ↦ (𝑓‘𝐴))
2		fvexd 6923	. 2 ⊢ (𝑓 ∈ V → (𝑓‘𝐴) ∈ V)
3	1, 2	fmpti 7136	1 ⊢ Slot 𝐴:V⟶V

This proof depends on syntax axioms:   ∈ wcel 2147  Vcvv 3454  ⟶wf 6554  ‘cfv 6558  Slot cslot 17388

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-10 2180  ax-11 2197  ax-12 2216  ax-ext 2735  ax-sep 5252  ax-nul 5263  ax-pr 5395

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-nf 1817  df-sb 2102  df-mo 2567  df-eu 2597  df-clab 2742  df-cleq 2755  df-clel 2839  df-nfc 2913  df-ne 2960  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-uni 4871  df-br 5107  df-opab 5171  df-mpt 5190  df-id 5550  df-xp 5661  df-rel 5662  df-cnv 5663  df-co 5664  df-dm 5665  df-rn 5666  df-res 5667  df-ima 5668  df-iota 6512  df-fun 6560  df-fn 6561  df-f 6562  df-fv 6566  df-slot 17389

This theorem is used by: (None)