Theorem bdcnulALT 16001

Description: Alternate proof of bdcnul 16000. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15979, or use the corresponding characterizations of its elements followed by bdelir 15982. (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 15992	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 15996	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3469	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 15979	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2776   \ cdif 3171   (/)c0 3468  BOUNDED wbdc 15975

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189  ax-bd0 15948  ax-bdim 15949  ax-bdan 15950  ax-bdn 15952  ax-bdeq 15955  ax-bdsb 15957

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-v 2778  df-dif 3176  df-nul 3469  df-bdc 15976

This theorem is referenced by: (None)