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Theorem iunordi 46082
Description: The indexed union of a collection of ordinal numbers 𝐵(𝑥) is ordinal. (Contributed by Emmett Weisz, 3-Nov-2019.)
Hypothesis
Ref Expression
iunordi.B Ord 𝐵
Assertion
Ref Expression
iunordi Ord 𝑥𝐴 𝐵
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem iunordi
StepHypRef Expression
1 iunord 46081 . 2 (∀𝑥𝐴 Ord 𝐵 → Ord 𝑥𝐴 𝐵)
2 iunordi.B . . 3 Ord 𝐵
32a1i 11 . 2 (𝑥𝐴 → Ord 𝐵)
41, 3mprg 3076 1 Ord 𝑥𝐴 𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2111   ciun 4918  Ord word 6229
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2159  ax-12 2176  ax-ext 2709  ax-sep 5206  ax-nul 5213  ax-pr 5336  ax-un 7541
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3or 1090  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-nf 1792  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-nfc 2887  df-ne 2942  df-ral 3067  df-rex 3068  df-rab 3071  df-v 3422  df-dif 3883  df-un 3885  df-in 3887  df-ss 3897  df-pss 3899  df-nul 4252  df-if 4454  df-sn 4556  df-pr 4558  df-tp 4560  df-op 4562  df-uni 4834  df-iun 4920  df-br 5068  df-opab 5130  df-tr 5176  df-eprel 5474  df-po 5482  df-so 5483  df-fr 5523  df-we 5525  df-ord 6233  df-on 6234
This theorem is referenced by: (None)
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