Theorem bdcnulALT 13053

Description: Alternate proof of bdcnul 13052. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13031, or use the corresponding characterizations of its elements followed by bdelir 13034. (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 13044	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 13048	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3359	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 13031	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2681   \ cdif 3063   (/)c0 3358  BOUNDED wbdc 13027

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119  ax-bd0 13000  ax-bdim 13001  ax-bdan 13002  ax-bdn 13004  ax-bdeq 13007  ax-bdsb 13009

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683  df-dif 3068  df-nul 3359  df-bdc 13028

This theorem is referenced by: (None)