Theorem bdcnulALT 15358

Description: Alternate proof of bdcnul 15357. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15336, or use the corresponding characterizations of its elements followed by bdelir 15339. (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 15349	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 15353	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3447	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 15336	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2760   ∖ cdif 3150  ∅c0 3446  BOUNDED wbdc 15332

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175  ax-bd0 15305  ax-bdim 15306  ax-bdan 15307  ax-bdn 15309  ax-bdeq 15312  ax-bdsb 15314

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762  df-dif 3155  df-nul 3447  df-bdc 15333

This theorem is referenced by: (None)