Theorem slotfn 17116

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 6894	. 2 ⊢ (𝑥‘𝑁) ∈ V
2		strfvnd.c	. . 3 ⊢ 𝐸 = Slot 𝑁
3		df-slot 17114	. . 3 ⊢ Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
4	2, 3	eqtri 2752	. 2 ⊢ 𝐸 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
5	1, 4	fnmpti 6683	1 ⊢ 𝐸 Fn V

Syntax hints:   = wceq 1533  Vcvv 3466   ↦ cmpt 5221   Fn wfn 6528  ‘cfv 6533  Slot cslot 17113

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-ne 2933  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-uni 4900  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-dm 5676  df-iota 6485  df-fun 6535  df-fn 6536  df-fv 6541  df-slot 17114

This theorem is referenced by:  basfn  17147  bj-isrvec  36665