Theorem bdcnulALT 16565

Description: Alternate proof of bdcnul 16564. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16543, or use the corresponding characterizations of its elements followed by bdelir 16546. (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 16556	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 16560	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3497	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 16543	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2803   ∖ cdif 3198  ∅c0 3496  BOUNDED wbdc 16539

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-ext 2213  ax-bd0 16512  ax-bdim 16513  ax-bdan 16514  ax-bdn 16516  ax-bdeq 16519  ax-bdsb 16521

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2805  df-dif 3203  df-nul 3497  df-bdc 16540

This theorem is referenced by: (None)