Theorem bdcnulALT 14187

Description: Alternate proof of bdcnul 14186. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 14165, or use the corresponding characterizations of its elements followed by bdelir 14168. (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 14178	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 14182	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3421	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 14165	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2735   ∖ cdif 3124  ∅c0 3420  BOUNDED wbdc 14161

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 1445  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-ext 2157  ax-bd0 14134  ax-bdim 14135  ax-bdan 14136  ax-bdn 14138  ax-bdeq 14141  ax-bdsb 14143

This theorem depends on definitions:  df-bi 117  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-v 2737  df-dif 3129  df-nul 3421  df-bdc 14162

This theorem is referenced by: (None)