Theorem bdcnulALT 15512

Description: Alternate proof of bdcnul 15511. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 15490, or use the corresponding characterizations of its elements followed by bdelir 15493. (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 15503	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 15507	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3451	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 15490	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2763   ∖ cdif 3154  ∅c0 3450  BOUNDED wbdc 15486

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-ext 2178  ax-bd0 15459  ax-bdim 15460  ax-bdan 15461  ax-bdn 15463  ax-bdeq 15466  ax-bdsb 15468

This theorem depends on definitions:  df-bi 117  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-v 2765  df-dif 3159  df-nul 3451  df-bdc 15487

This theorem is referenced by: (None)