Theorem bdcnulALT 16582

Description: Alternate proof of bdcnul 16581. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16560, or use the corresponding characterizations of its elements followed by bdelir 16563. (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 16573	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 16577	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3497	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 16560	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2803   \ cdif 3198   (/)c0 3496  BOUNDED wbdc 16556

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-ext 2213  ax-bd0 16529  ax-bdim 16530  ax-bdan 16531  ax-bdn 16533  ax-bdeq 16536  ax-bdsb 16538

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2805  df-dif 3203  df-nul 3497  df-bdc 16557

This theorem is referenced by: (None)