ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  omsson Structured version   GIF version

Theorem omsson 4278
Description: Omega is a subset of On. (Contributed by NM, 13-Jun-1994.)
Assertion
Ref Expression
omsson 𝜔 ⊆ On

Proof of Theorem omsson
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 nnon 4275 . 2 (x 𝜔 → x On)
21ssriv 2943 1 𝜔 ⊆ On
Colors of variables: wff set class
Syntax hints:  wss 2911  Oncon0 4066  𝜔com 4256
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-nul 3874  ax-pow 3918  ax-pr 3935  ax-un 4136  ax-iinf 4254
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-pw 3353  df-sn 3373  df-pr 3374  df-uni 3572  df-int 3607  df-tr 3846  df-iord 4069  df-on 4071  df-suc 4074  df-iom 4257
This theorem is referenced by:  frecfnom  5925  frecrdg  5931  dmaddpi  6309  dmmulpi  6310
  Copyright terms: Public domain W3C validator