Theorem bdcnulALT 13901

Description: Alternate proof of bdcnul 13900. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13879, or use the corresponding characterizations of its elements followed by bdelir 13882. (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 13892	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 13896	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3415	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 13879	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2730   ∖ cdif 3118  ∅c0 3414  BOUNDED wbdc 13875

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152  ax-bd0 13848  ax-bdim 13849  ax-bdan 13850  ax-bdn 13852  ax-bdeq 13855  ax-bdsb 13857

This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732  df-dif 3123  df-nul 3415  df-bdc 13876

This theorem is referenced by: (None)