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Theorem fset0 8795
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 6726 . . 3 (𝑓:∅⟶𝐵𝑓 = ∅)
21abbii 2803 . 2 {𝑓𝑓:∅⟶𝐵} = {𝑓𝑓 = ∅}
3 df-sn 4588 . 2 {∅} = {𝑓𝑓 = ∅}
42, 3eqtr4i 2764 1 {𝑓𝑓:∅⟶𝐵} = {∅}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {cab 2710  c0 4283  {csn 4587  wf 6493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5257  ax-nul 5264  ax-pr 5385
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-id 5532  df-xp 5640  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-fun 6499  df-fn 6500  df-f 6501
This theorem is referenced by:  fsetexb  8805
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