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Theorem en1unielOLD 8794
Description: Obsolete version of en1uniel 8793 as of 24-Sep-2024. (Contributed by Stefan O'Rear, 16-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
en1unielOLD (𝑆 ≈ 1o 𝑆𝑆)

Proof of Theorem en1unielOLD
StepHypRef Expression
1 relen 8713 . . . 4 Rel ≈
21brrelex1i 5643 . . 3 (𝑆 ≈ 1o𝑆 ∈ V)
3 uniexg 7585 . . 3 (𝑆 ∈ V → 𝑆 ∈ V)
4 snidg 4601 . . 3 ( 𝑆 ∈ V → 𝑆 ∈ { 𝑆})
52, 3, 43syl 18 . 2 (𝑆 ≈ 1o 𝑆 ∈ { 𝑆})
6 en1b 8788 . . 3 (𝑆 ≈ 1o𝑆 = { 𝑆})
76biimpi 215 . 2 (𝑆 ≈ 1o𝑆 = { 𝑆})
85, 7eleqtrrd 2844 1 (𝑆 ≈ 1o 𝑆𝑆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1542  wcel 2110  Vcvv 3431  {csn 4567   cuni 4845   class class class wbr 5079  1oc1o 8275  cen 8705
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2158  ax-12 2175  ax-ext 2711  ax-sep 5227  ax-nul 5234  ax-pr 5356  ax-un 7580
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-nf 1791  df-sb 2072  df-mo 2542  df-eu 2571  df-clab 2718  df-cleq 2732  df-clel 2818  df-nfc 2891  df-ne 2946  df-ral 3071  df-rex 3072  df-reu 3073  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4846  df-br 5080  df-opab 5142  df-id 5489  df-xp 5595  df-rel 5596  df-cnv 5597  df-co 5598  df-dm 5599  df-rn 5600  df-res 5601  df-ima 5602  df-suc 6270  df-iota 6389  df-fun 6433  df-fn 6434  df-f 6435  df-f1 6436  df-fo 6437  df-f1o 6438  df-fv 6439  df-1o 8282  df-en 8709
This theorem is referenced by: (None)
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