Theorem bdcnulALT 14914

Description: Alternate proof of bdcnul 14913. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 14892, or use the corresponding characterizations of its elements followed by bdelir 14895. (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 14905	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 14909	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3435	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 14892	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2749   \ cdif 3138   (/)c0 3434  BOUNDED wbdc 14888

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-ext 2169  ax-bd0 14861  ax-bdim 14862  ax-bdan 14863  ax-bdn 14865  ax-bdeq 14868  ax-bdsb 14870

This theorem depends on definitions:  df-bi 117  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-v 2751  df-dif 3143  df-nul 3435  df-bdc 14889

This theorem is referenced by: (None)