Theorem bdcnulALT 13235

Description: Alternate proof of bdcnul 13234. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13213, or use the corresponding characterizations of its elements followed by bdelir 13216. (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 13226	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 13230	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3369	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 13213	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2689   ∖ cdif 3073  ∅c0 3368  BOUNDED wbdc 13209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122  ax-bd0 13182  ax-bdim 13183  ax-bdan 13184  ax-bdn 13186  ax-bdeq 13189  ax-bdsb 13191

This theorem depends on definitions:  df-bi 116  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-v 2691  df-dif 3078  df-nul 3369  df-bdc 13210

This theorem is referenced by: (None)