Theorem bdcnulALT 16892

Description: Alternate proof of bdcnul 16891. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16870, or use the corresponding characterizations of its elements followed by bdelir 16873. (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 16883	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 16887	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3521	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 16870	1 |- BOUNDED (/)

This proof depends on syntax axioms:   _Vcvv 2821   \ cdif 3217   (/)c0 3520  BOUNDED wbdc 16866

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220  ax-bd0 16839  ax-bdim 16840  ax-bdan 16841  ax-bdn 16843  ax-bdeq 16846  ax-bdsb 16848

This proof depends on definitions:  df-bi 117  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823  df-dif 3222  df-nul 3521  df-bdc 16867

This theorem is used by: (None)