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

Theorem bj-omssonALT 10901
Description: Alternate proof of bj-omsson 10900. (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 10899 . 2 ω ∈ On
2 onss 4239 . 2 (ω ∈ On → ω ⊆ On)
31, 2ax-mp 7 1 ω ⊆ On
Colors of variables: wff set class
Syntax hints:  wcel 1434  wss 2974  Oncon0 4120  ωcom 4333
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-nul 3906  ax-pr 3966  ax-un 4190  ax-bd0 10747  ax-bdor 10750  ax-bdal 10752  ax-bdex 10753  ax-bdeq 10754  ax-bdel 10755  ax-bdsb 10756  ax-bdsep 10818  ax-infvn 10879
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-rab 2358  df-v 2604  df-dif 2976  df-un 2978  df-in 2980  df-ss 2987  df-nul 3253  df-sn 3406  df-pr 3407  df-uni 3604  df-int 3639  df-tr 3878  df-iord 4123  df-on 4125  df-suc 4128  df-iom 4334  df-bdc 10775  df-bj-ind 10865
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator