Theorem bdcnulALT 9986

Description: Alternate proof of bdcnul 9985. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 9964, or use the corresponding characterizations of its elements followed by bdelir 9967. (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 9977	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 9981	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3225	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 9964	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2557   ∖ cdif 2914  ∅c0 3224  BOUNDED wbdc 9960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdim 9934  ax-bdan 9935  ax-bdn 9937  ax-bdeq 9940  ax-bdsb 9942

This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-dif 2920  df-nul 3225  df-bdc 9961

This theorem is referenced by: (None)