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Theorem onnoi 43398
Description: Every ordinal maps to a surreal number. (Contributed by RP, 21-Sep-2023.)
Hypothesis
Ref Expression
onnoi.on 𝐴 ∈ On
Assertion
Ref Expression
onnoi (𝐴 × {2o}) ∈ No

Proof of Theorem onnoi
StepHypRef Expression
1 onnoi.on . 2 𝐴 ∈ On
2 onno 43397 . 2 (𝐴 ∈ On → (𝐴 × {2o}) ∈ No )
31, 2ax-mp 5 1 (𝐴 × {2o}) ∈ No
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  {csn 4648   × cxp 5698  Oncon0 6397  2oc2o 8518   No csur 27704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2158  ax-12 2178  ax-ext 2711  ax-sep 5317  ax-nul 5324  ax-pow 5383  ax-pr 5447  ax-un 7772
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-nf 1782  df-sb 2065  df-mo 2543  df-eu 2572  df-clab 2718  df-cleq 2732  df-clel 2819  df-nfc 2895  df-ne 2947  df-ral 3068  df-rex 3077  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-in 3983  df-ss 3993  df-nul 4353  df-if 4549  df-pw 4624  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-opab 5229  df-mpt 5250  df-id 5593  df-xp 5706  df-rel 5707  df-cnv 5708  df-co 5709  df-dm 5710  df-rn 5711  df-suc 6403  df-fun 6577  df-fn 6578  df-f 6579  df-1o 8524  df-2o 8525  df-no 27707
This theorem is referenced by:  0no  43399  1no  43400  2no  43401  3no  43402  4no  43403
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