Theorem bdcnulALT 13708

Description: Alternate proof of bdcnul 13707. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13686, or use the corresponding characterizations of its elements followed by bdelir 13689. (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 13699	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 13703	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3409	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 13686	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2725   ∖ cdif 3112  ∅c0 3408  BOUNDED wbdc 13682

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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147  ax-bd0 13655  ax-bdim 13656  ax-bdan 13657  ax-bdn 13659  ax-bdeq 13662  ax-bdsb 13664

This theorem depends on definitions:  df-bi 116  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2727  df-dif 3117  df-nul 3409  df-bdc 13683

This theorem is referenced by: (None)