Theorem slotfn 17122

Description: A slot is a function on sets, treated as structures. (Contributed by Mario Carneiro, 22-Sep-2015.)

Hypothesis

Ref	Expression
strfvnd.c	⊢ 𝐸 = Slot 𝑁

Assertion

Ref	Expression
slotfn	⊢ 𝐸 Fn V

Proof of Theorem slotfn

Dummy variable 𝑥 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		fvex 6895	. 2 ⊢ (𝑥‘𝑁) ∈ V
2		strfvnd.c	. . 3 ⊢ 𝐸 = Slot 𝑁
3		df-slot 17120	. . 3 ⊢ Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
4	2, 3	eqtri 2752	. 2 ⊢ 𝐸 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
5	1, 4	fnmpti 6684	1 ⊢ 𝐸 Fn V

Syntax hints:   = wceq 1533  Vcvv 3466   ↦ cmpt 5222   Fn wfn 6529  ‘cfv 6534  Slot cslot 17119

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 5290  ax-nul 5297  ax-pr 5418

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-ne 2933  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-opab 5202  df-mpt 5223  df-id 5565  df-xp 5673  df-rel 5674  df-cnv 5675  df-co 5676  df-dm 5677  df-iota 6486  df-fun 6536  df-fn 6537  df-fv 6542  df-slot 17120

This theorem is referenced by:  basfn  17153  bj-isrvec  36676