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Theorem fset0 8873
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 6780 . . 3 (𝑓:∅⟶𝐵𝑓 = ∅)
21abbii 2798 . 2 {𝑓𝑓:∅⟶𝐵} = {𝑓𝑓 = ∅}
3 df-sn 4630 . 2 {∅} = {𝑓𝑓 = ∅}
42, 3eqtr4i 2759 1 {𝑓𝑓:∅⟶𝐵} = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  {cab 2705  c0 4323  {csn 4629  wf 6544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-10 2130  ax-11 2147  ax-12 2167  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-3an 1087  df-tru 1537  df-fal 1547  df-ex 1775  df-nf 1779  df-sb 2061  df-mo 2530  df-clab 2706  df-cleq 2720  df-clel 2806  df-ral 3059  df-rex 3068  df-rab 3430  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5149  df-opab 5211  df-id 5576  df-xp 5684  df-rel 5685  df-cnv 5686  df-co 5687  df-dm 5688  df-rn 5689  df-fun 6550  df-fn 6551  df-f 6552
This theorem is referenced by:  fsetexb  8883
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