Theorem bdcnulALT 15940

Description: Alternate proof of bdcnul 15939. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15918, or use the corresponding characterizations of its elements followed by bdelir 15921. (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 15931	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 15935	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3465	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 15918	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2773   ∖ cdif 3167  ∅c0 3464  BOUNDED wbdc 15914

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2188  ax-bd0 15887  ax-bdim 15888  ax-bdan 15889  ax-bdn 15891  ax-bdeq 15894  ax-bdsb 15896

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-v 2775  df-dif 3172  df-nul 3465  df-bdc 15915

This theorem is referenced by: (None)