Theorem slotfn 16503

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 6685	. 2 ⊢ (𝑥‘𝑁) ∈ V
2		strfvnd.c	. . 3 ⊢ 𝐸 = Slot 𝑁
3		df-slot 16489	. . 3 ⊢ Slot 𝑁 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
4	2, 3	eqtri 2846	. 2 ⊢ 𝐸 = (𝑥 ∈ V ↦ (𝑥‘𝑁))
5	1, 4	fnmpti 6493	1 ⊢ 𝐸 Fn V

Syntax hints:   = wceq 1537  Vcvv 3496   ↦ cmpt 5148   Fn wfn 6352  ‘cfv 6357  Slot cslot 16484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2795  ax-sep 5205  ax-nul 5212  ax-pr 5332

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-mo 2622  df-eu 2654  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-ral 3145  df-rex 3146  df-rab 3149  df-v 3498  df-sbc 3775  df-dif 3941  df-un 3943  df-in 3945  df-ss 3954  df-nul 4294  df-if 4470  df-sn 4570  df-pr 4572  df-op 4576  df-uni 4841  df-br 5069  df-opab 5131  df-mpt 5149  df-id 5462  df-xp 5563  df-rel 5564  df-cnv 5565  df-co 5566  df-dm 5567  df-iota 6316  df-fun 6359  df-fn 6360  df-fv 6365  df-slot 16489

This theorem is referenced by:  basfn  16505