Theorem bdcnulALT 14758

Description: Alternate proof of bdcnul 14757. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 14736, or use the corresponding characterizations of its elements followed by bdelir 14739. (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 14749	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 14753	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3425	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 14736	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2739   ∖ cdif 3128  ∅c0 3424  BOUNDED wbdc 14732

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159  ax-bd0 14705  ax-bdim 14706  ax-bdan 14707  ax-bdn 14709  ax-bdeq 14712  ax-bdsb 14714

This theorem depends on definitions:  df-bi 117  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2741  df-dif 3133  df-nul 3425  df-bdc 14733

This theorem is referenced by: (None)