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Theorem permsetexOLD 19323
Description: Obsolete version of f1osetex 8871 as of 8-Aug-2024. (Contributed by AV, 30-Mar-2024.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
permsetexOLD (𝐴𝑉 → {𝑓𝑓:𝐴1-1-onto𝐴} ∈ V)
Distinct variable group:   𝐴,𝑓
Allowed substitution hint:   𝑉(𝑓)

Proof of Theorem permsetexOLD
StepHypRef Expression
1 mapex 8844 . . 3 ((𝐴𝑉𝐴𝑉) → {𝑓𝑓:𝐴𝐴} ∈ V)
21anidms 565 . 2 (𝐴𝑉 → {𝑓𝑓:𝐴𝐴} ∈ V)
3 f1of 6832 . . . 4 (𝑓:𝐴1-1-onto𝐴𝑓:𝐴𝐴)
43ss2abi 4056 . . 3 {𝑓𝑓:𝐴1-1-onto𝐴} ⊆ {𝑓𝑓:𝐴𝐴}
54a1i 11 . 2 (𝐴𝑉 → {𝑓𝑓:𝐴1-1-onto𝐴} ⊆ {𝑓𝑓:𝐴𝐴})
62, 5ssexd 5320 1 (𝐴𝑉 → {𝑓𝑓:𝐴1-1-onto𝐴} ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2098  {cab 2702  Vcvv 3463  wss 3941  wf 6539  1-1-ontowf1o 6542
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-ext 2696  ax-sep 5295  ax-nul 5302  ax-pow 5360  ax-pr 5424  ax-un 7735
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ral 3052  df-rex 3061  df-rab 3420  df-v 3465  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4320  df-if 4526  df-pw 4601  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4905  df-br 5145  df-opab 5207  df-xp 5679  df-rel 5680  df-cnv 5681  df-dm 5683  df-rn 5684  df-fun 6545  df-fn 6546  df-f 6547  df-f1 6548  df-f1o 6550
This theorem is referenced by:  symgbasexOLD  19325
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