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Theorem bj-omssonALT 15379
Description: Alternate proof of bj-omsson 15378. (Contributed by BJ, 27-Oct-2020.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-omssonALT ω ⊆ On

Proof of Theorem bj-omssonALT
StepHypRef Expression
1 bj-omelon 15377 . 2 ω ∈ On
2 onss 4517 . 2 (ω ∈ On → ω ⊆ On)
31, 2ax-mp 5 1 ω ⊆ On
Colors of variables: wff set class
Syntax hints:  wcel 2160  wss 3149  Oncon0 4388  ωcom 4614
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-13 2162  ax-14 2163  ax-ext 2171  ax-nul 4151  ax-pr 4234  ax-un 4458  ax-bd0 15229  ax-bdor 15232  ax-bdal 15234  ax-bdex 15235  ax-bdeq 15236  ax-bdel 15237  ax-bdsb 15238  ax-bdsep 15300  ax-infvn 15357
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-rab 2477  df-v 2758  df-dif 3151  df-un 3153  df-in 3155  df-ss 3162  df-nul 3443  df-sn 3620  df-pr 3621  df-uni 3832  df-int 3867  df-tr 4124  df-iord 4391  df-on 4393  df-suc 4396  df-iom 4615  df-bdc 15257  df-bj-ind 15343
This theorem is referenced by: (None)
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