Theorem bdcnulALT 15806

Description: Alternate proof of bdcnul 15805. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15784, or use the corresponding characterizations of its elements followed by bdelir 15787. (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 15797	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 15801	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3461	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 15784	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2772   \ cdif 3163   (/)c0 3460  BOUNDED wbdc 15780

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-ext 2187  ax-bd0 15753  ax-bdim 15754  ax-bdan 15755  ax-bdn 15757  ax-bdeq 15760  ax-bdsb 15762

This theorem depends on definitions:  df-bi 117  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774  df-dif 3168  df-nul 3461  df-bdc 15781

This theorem is referenced by: (None)