Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-omsson GIF version

Theorem bj-omsson 15392
Description: Constructive proof of omsson 4641. See also bj-omssonALT 15393. (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 15389 . 2 (𝑥 ∈ ω → 𝑥 ∈ On)
21ssriv 3183 1 ω ⊆ On
Colors of variables: wff set class
Syntax hints:  wss 3153  Oncon0 4392  ωcom 4618
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 2166  ax-14 2167  ax-ext 2175  ax-nul 4155  ax-pr 4238  ax-un 4462  ax-bd0 15243  ax-bdor 15246  ax-bdal 15248  ax-bdex 15249  ax-bdeq 15250  ax-bdel 15251  ax-bdsb 15252  ax-bdsep 15314  ax-infvn 15371
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-rex 2478  df-rab 2481  df-v 2762  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3447  df-sn 3624  df-pr 3625  df-uni 3836  df-int 3871  df-tr 4128  df-iord 4395  df-on 4397  df-suc 4400  df-iom 4619  df-bdc 15271  df-bj-ind 15357
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator