Theorem bdcnulALT 13064

Description: Alternate proof of bdcnul 13063. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13042, or use the corresponding characterizations of its elements followed by bdelir 13045. (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 13055	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 13059	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3364	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 13042	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2686   ∖ cdif 3068  ∅c0 3363  BOUNDED wbdc 13038

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121  ax-bd0 13011  ax-bdim 13012  ax-bdan 13013  ax-bdn 13015  ax-bdeq 13018  ax-bdsb 13020

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688  df-dif 3073  df-nul 3364  df-bdc 13039

This theorem is referenced by: (None)