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

Theorem bdcnulALT 11414
Description: Alternate proof of bdcnul 11413. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 11392, or use the corresponding characterizations of its elements followed by bdelir 11395. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bdcnulALT BOUNDED

Proof of Theorem bdcnulALT
StepHypRef Expression
1 bdcvv 11405 . . 3 BOUNDED V
21, 1bdcdif 11409 . 2 BOUNDED (V ∖ V)
3 df-nul 3285 . 2 ∅ = (V ∖ V)
42, 3bdceqir 11392 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  Vcvv 2619  cdif 2994  c0 3284  BOUNDED wbdc 11388
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-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070  ax-bd0 11361  ax-bdim 11362  ax-bdan 11363  ax-bdn 11365  ax-bdeq 11368  ax-bdsb 11370
This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621  df-dif 2999  df-nul 3285  df-bdc 11389
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator