Theorem bdcnulALT 10657

Description: Alternate proof of bdcnul 10656. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 10635, or use the corresponding characterizations of its elements followed by bdelir 10638. (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 10648	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 10652	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3252	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 10635	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2601   ∖ cdif 2970  ∅c0 3251  BOUNDED wbdc 10631

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063  ax-bd0 10604  ax-bdim 10605  ax-bdan 10606  ax-bdn 10608  ax-bdeq 10611  ax-bdsb 10613

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603  df-dif 2975  df-nul 3252  df-bdc 10632

This theorem is referenced by: (None)