Theorem bdcnulALT 16187

Description: Alternate proof of bdcnul 16186. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16165, or use the corresponding characterizations of its elements followed by bdelir 16168. (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 16178	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 16182	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3492	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 16165	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2799   ∖ cdif 3194  ∅c0 3491  BOUNDED wbdc 16161

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-ext 2211  ax-bd0 16134  ax-bdim 16135  ax-bdan 16136  ax-bdn 16138  ax-bdeq 16141  ax-bdsb 16143

This theorem depends on definitions:  df-bi 117  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-v 2801  df-dif 3199  df-nul 3492  df-bdc 16162

This theorem is referenced by: (None)