Theorem bdcnulALT 13758

Description: Alternate proof of bdcnul 13757. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13736, or use the corresponding characterizations of its elements followed by bdelir 13739. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bdcnulALT	|- BOUNDED (/)

Proof of Theorem bdcnulALT

Step	Hyp	Ref	Expression
1		bdcvv 13749	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 13753	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3410	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 13736	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2726   \ cdif 3113   (/)c0 3409  BOUNDED wbdc 13732

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147  ax-bd0 13705  ax-bdim 13706  ax-bdan 13707  ax-bdn 13709  ax-bdeq 13712  ax-bdsb 13714

This theorem depends on definitions:  df-bi 116  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2728  df-dif 3118  df-nul 3410  df-bdc 13733

This theorem is referenced by: (None)