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Theorem onun2i 4336
Description: The union of two ordinal numbers is an ordinal number. (Contributed by NM, 13-Jun-1994.) (Constructive proof by Jim Kingdon, 25-Jul-2019.)
Hypotheses
Ref Expression
onun2i.1  |-  A  e.  On
onun2i.2  |-  B  e.  On
Assertion
Ref Expression
onun2i  |-  ( A  u.  B )  e.  On

Proof of Theorem onun2i
StepHypRef Expression
1 onun2i.1 . 2  |-  A  e.  On
2 onun2i.2 . 2  |-  B  e.  On
3 onun2 4335 . 2  |-  ( ( A  e.  On  /\  B  e.  On )  ->  ( A  u.  B
)  e.  On )
41, 2, 3mp2an 418 1  |-  ( A  u.  B )  e.  On
Colors of variables: wff set class
Syntax hints:    e. wcel 1445    u. cun 3011   Oncon0 4214
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-13 1456  ax-14 1457  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978  ax-pr 4060  ax-un 4284
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rex 2376  df-v 2635  df-un 3017  df-in 3019  df-ss 3026  df-sn 3472  df-pr 3473  df-uni 3676  df-tr 3959  df-iord 4217  df-on 4219
This theorem is referenced by: (None)
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