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Theorem df3o3 43327
Description: Ordinal 3, fully expanded. (Contributed by RP, 8-Jul-2021.)
Assertion
Ref Expression
df3o3 3o = {∅, {∅}, {∅, {∅}}}

Proof of Theorem df3o3
StepHypRef Expression
1 df-3o 8508 . 2 3o = suc 2o
2 df2o2 8515 . . . 4 2o = {∅, {∅}}
32sneqi 4637 . . . 4 {2o} = {{∅, {∅}}}
42, 3uneq12i 4166 . . 3 (2o ∪ {2o}) = ({∅, {∅}} ∪ {{∅, {∅}}})
5 df-suc 6390 . . 3 suc 2o = (2o ∪ {2o})
6 df-tp 4631 . . 3 {∅, {∅}, {∅, {∅}}} = ({∅, {∅}} ∪ {{∅, {∅}}})
74, 5, 63eqtr4i 2775 . 2 suc 2o = {∅, {∅}, {∅, {∅}}}
81, 7eqtri 2765 1 3o = {∅, {∅}, {∅, {∅}}}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cun 3949  c0 4333  {csn 4626  {cpr 4628  {ctp 4630  suc csuc 6386  2oc2o 8500  3oc3o 8501
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334  df-sn 4627  df-pr 4629  df-tp 4631  df-suc 6390  df-1o 8506  df-2o 8507  df-3o 8508
This theorem is referenced by: (None)
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