Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-inf2vn2 Unicode version

Theorem bj-inf2vn2 9435
Description: A sufficient condition for  om to be a set; unbounded version of bj-inf2vn 9434. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-inf2vn2  V  (/)  suc  om
Distinct variable group:   ,,
Allowed substitution hints:    V(,)

Proof of Theorem bj-inf2vn2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bj-inf2vnlem1 9430 . . 3  (/)  suc Ind
2 bi1 111 . . . . . . 7  (/)  suc  (/)  suc
32alimi 1341 . . . . . 6  (/)  suc  (/)  suc
4 df-ral 2305 . . . . . 6  (/)  suc  (/)  suc
53, 4sylibr 137 . . . . 5  (/)  suc  (/)  suc
6 bj-inf2vnlem4 9433 . . . . 5  (/)  suc Ind  C_
75, 6syl 14 . . . 4  (/)  suc Ind  C_
87alrimiv 1751 . . 3  (/)  suc Ind  C_
91, 8jca 290 . 2  (/)  suc Ind Ind 
C_
10 bj-om 9396 . 2  V  om Ind Ind  C_
119, 10syl5ibr 145 1  V  (/)  suc  om
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wo 628  wal 1240   wceq 1242   wcel 1390  wral 2300  wrex 2301    C_ wss 2911   (/)c0 3218   suc csuc 4068   omcom 4256  Ind wind 9385
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-bndl 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-nul 3874  ax-pr 3935  ax-un 4136  ax-setind 4220  ax-bd0 9268  ax-bdor 9271  ax-bdex 9274  ax-bdeq 9275  ax-bdel 9276  ax-bdsb 9277  ax-bdsep 9339
This theorem depends on definitions:  df-bi 110  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-rab 2309  df-v 2553  df-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-pr 3374  df-uni 3572  df-int 3607  df-suc 4074  df-iom 4257  df-bdc 9296  df-bj-ind 9386
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator