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Theorem fosetex 8604
Description: The set of surjections between two classes exists (without any precondition). (Contributed by AV, 8-Aug-2024.)
Assertion
Ref Expression
fosetex {𝑓𝑓:𝐴onto𝐵} ∈ V
Distinct variable groups:   𝐴,𝑓   𝐵,𝑓

Proof of Theorem fosetex
StepHypRef Expression
1 ovex 7288 . 2 (𝐵m 𝐴) ∈ V
2 mapfoss 8598 . 2 {𝑓𝑓:𝐴onto𝐵} ⊆ (𝐵m 𝐴)
31, 2ssexi 5241 1 {𝑓𝑓:𝐴onto𝐵} ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  {cab 2715  Vcvv 3422  ontowfo 6416  (class class class)co 7255  m cmap 8573
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2156  ax-12 2173  ax-ext 2709  ax-sep 5218  ax-nul 5225  ax-pow 5283  ax-pr 5347  ax-un 7566
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-nf 1788  df-sb 2069  df-mo 2540  df-eu 2569  df-clab 2716  df-cleq 2730  df-clel 2817  df-nfc 2888  df-ral 3068  df-rex 3069  df-rab 3072  df-v 3424  df-sbc 3712  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-if 4457  df-pw 4532  df-sn 4559  df-pr 4561  df-op 4565  df-uni 4837  df-br 5071  df-opab 5133  df-id 5480  df-xp 5586  df-rel 5587  df-cnv 5588  df-co 5589  df-dm 5590  df-rn 5591  df-iota 6376  df-fun 6420  df-fn 6421  df-f 6422  df-fo 6424  df-fv 6426  df-ov 7258  df-oprab 7259  df-mpo 7260  df-map 8575
This theorem is referenced by:  f1osetex  8605
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