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Theorem limuni2 4191
Description: The union of a limit ordinal is a limit ordinal. (Contributed by NM, 19-Sep-2006.)
Assertion
Ref Expression
limuni2 (Lim 𝐴 → Lim 𝐴)

Proof of Theorem limuni2
StepHypRef Expression
1 limuni 4190 . . 3 (Lim 𝐴𝐴 = 𝐴)
2 limeq 4171 . . 3 (𝐴 = 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
31, 2syl 14 . 2 (Lim 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
43ibi 174 1 (Lim 𝐴 → Lim 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103   = wceq 1287   cuni 3630  Lim wlim 4158
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-in 2992  df-ss 2999  df-uni 3631  df-tr 3905  df-iord 4160  df-ilim 4163
This theorem is referenced by: (None)
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