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Theorem bj-omsson 14717
Description: Constructive proof of omsson 4613. See also bj-omssonALT 14718. (Contributed by BJ, 27-Oct-2020.) (Proof modification is discouraged.) (New usage is discouraged.
Assertion
Ref Expression
bj-omsson ω ⊆ On

Proof of Theorem bj-omsson
StepHypRef Expression
1 bj-nnelon 14714 . 2 (𝑥 ∈ ω → 𝑥 ∈ On)
21ssriv 3160 1 ω ⊆ On
Colors of variables: wff set class
Syntax hints:  wss 3130  Oncon0 4364  ωcom 4590
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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-nul 4130  ax-pr 4210  ax-un 4434  ax-bd0 14568  ax-bdor 14571  ax-bdal 14573  ax-bdex 14574  ax-bdeq 14575  ax-bdel 14576  ax-bdsb 14577  ax-bdsep 14639  ax-infvn 14696
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-ral 2460  df-rex 2461  df-rab 2464  df-v 2740  df-dif 3132  df-un 3134  df-in 3136  df-ss 3143  df-nul 3424  df-sn 3599  df-pr 3600  df-uni 3811  df-int 3846  df-tr 4103  df-iord 4367  df-on 4369  df-suc 4372  df-iom 4591  df-bdc 14596  df-bj-ind 14682
This theorem is referenced by: (None)
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