Theorem bdssexi 16266

Description: Bounded version of ssexi 4222. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bdssexi.bd	|- BOUNDED A
bdssexi.1	|- B e. _V
bdssexi.2	|- A C_ B

Assertion

Ref	Expression
bdssexi	|- A e. _V

Proof of Theorem bdssexi

Step	Hyp	Ref	Expression
1		bdssexi.2	. 2 |- A C_ B
2		bdssexi.bd	. . 3 |- BOUNDED A
3		bdssexi.1	. . 3 |- B e. _V
4	2, 3	bdssex 16265	. 2 |- ( A C_ B -> A e. _V )
5	1, 4	ax-mp 5	1 |- A e. _V

Syntax hints:   e. wcel 2200   _Vcvv 2799   C_ wss 3197  BOUNDED wbdc 16203

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-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-bdsep 16247

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-in 3203  df-ss 3210  df-bdc 16204

This theorem is referenced by: (None)