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Theorem iunordi 43211
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 43210 . 2 (∀𝑥𝐴 Ord 𝐵 → Ord 𝑥𝐴 𝐵)
2 iunordi.B . . 3 Ord 𝐵
32a1i 11 . 2 (𝑥𝐴 → Ord 𝐵)
41, 3mprg 3106 1 Ord 𝑥𝐴 𝐵
Colors of variables: wff setvar class
Syntax hints:  wcel 2157   ciun 4709  Ord word 5939
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-8 2159  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2776  ax-sep 4974  ax-nul 4982  ax-pr 5096  ax-un 7182
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-3or 1109  df-3an 1110  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-mo 2591  df-eu 2609  df-clab 2785  df-cleq 2791  df-clel 2794  df-nfc 2929  df-ne 2971  df-ral 3093  df-rex 3094  df-rab 3097  df-v 3386  df-sbc 3633  df-dif 3771  df-un 3773  df-in 3775  df-ss 3782  df-pss 3784  df-nul 4115  df-if 4277  df-sn 4368  df-pr 4370  df-tp 4372  df-op 4374  df-uni 4628  df-iun 4711  df-br 4843  df-opab 4905  df-tr 4945  df-eprel 5224  df-po 5232  df-so 5233  df-fr 5270  df-we 5272  df-ord 5943  df-on 5944
This theorem is referenced by: (None)
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