Theorem bdcnulALT 16806

Description: Alternate proof of bdcnul 16805. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16784, or use the corresponding characterizations of its elements followed by bdelir 16787. (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 16797	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 16801	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3521	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 16784	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2821   ∖ cdif 3217  ∅c0 3520  BOUNDED wbdc 16780

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220  ax-bd0 16753  ax-bdim 16754  ax-bdan 16755  ax-bdn 16757  ax-bdeq 16760  ax-bdsb 16762

This theorem depends on definitions:  df-bi 117  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823  df-dif 3222  df-nul 3521  df-bdc 16781

This theorem is referenced by: (None)