Theorem bdcnulALT 15666

Description: Alternate proof of bdcnul 15665. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15644, or use the corresponding characterizations of its elements followed by bdelir 15647. (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 15657	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 15661	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3460	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 15644	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2771   ∖ cdif 3162  ∅c0 3459  BOUNDED wbdc 15640

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-ext 2186  ax-bd0 15613  ax-bdim 15614  ax-bdan 15615  ax-bdn 15617  ax-bdeq 15620  ax-bdsb 15622

This theorem depends on definitions:  df-bi 117  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-v 2773  df-dif 3167  df-nul 3460  df-bdc 15641

This theorem is referenced by: (None)