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Theorem fset0 8845
Description: The set of functions from the empty set is the singleton containing the empty set. (Contributed by AV, 13-Sep-2024.)
Assertion
Ref Expression
fset0 {𝑓𝑓:∅⟶𝐵} = {∅}

Proof of Theorem fset0
StepHypRef Expression
1 f0bi 6765 . . 3 (𝑓:∅⟶𝐵𝑓 = ∅)
21abbii 2794 . 2 {𝑓𝑓:∅⟶𝐵} = {𝑓𝑓 = ∅}
3 df-sn 4622 . 2 {∅} = {𝑓𝑓 = ∅}
42, 3eqtr4i 2755 1 {𝑓𝑓:∅⟶𝐵} = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  {cab 2701  c0 4315  {csn 4621  wf 6530
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-clab 2702  df-cleq 2716  df-clel 2802  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-br 5140  df-opab 5202  df-id 5565  df-xp 5673  df-rel 5674  df-cnv 5675  df-co 5676  df-dm 5677  df-rn 5678  df-fun 6536  df-fn 6537  df-f 6538
This theorem is referenced by:  fsetexb  8855
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