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Mirrors > Home > MPE Home > Th. List > omsson | Structured version Visualization version GIF version |
Description: Omega is a subset of On. (Contributed by NM, 13-Jun-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
omsson | ⊢ ω ⊆ On |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-om 7808 | . 2 ⊢ ω = {𝑥 ∈ On ∣ ∀𝑦(Lim 𝑦 → 𝑥 ∈ 𝑦)} | |
2 | 1 | ssrab3 4045 | 1 ⊢ ω ⊆ On |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 ⊆ wss 3915 Oncon0 6322 Lim wlim 6323 ωcom 7807 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-rab 3411 df-v 3450 df-in 3922 df-ss 3932 df-om 7808 |
This theorem is referenced by: limomss 7812 nnon 7813 ordom 7817 omssnlim 7822 omsinds 7828 omsindsOLD 7829 nnunifi 9245 unblem1 9246 unblem2 9247 unblem3 9248 unblem4 9249 isfinite2 9252 card2inf 9498 ackbij1lem16 10178 ackbij1lem18 10180 fin23lem26 10268 fin23lem27 10271 isf32lem5 10300 fin1a2lem6 10348 pwfseqlem3 10603 tskinf 10712 grothomex 10772 ltsopi 10831 dmaddpi 10833 dmmulpi 10834 2ndcdisj 22823 finminlem 34819 cantnftermord 41684 omabs2 41696 |
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