Theorem bdssexi 15052

Description: Bounded version of ssexi 4156. (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 15051	. 2 |- ( A C_ B -> A e. _V )
5	1, 4	ax-mp 5	1 |- A e. _V

Syntax hints:   e. wcel 2160   _Vcvv 2752   C_ wss 3144  BOUNDED wbdc 14989

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-bdsep 15033

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150  df-ss 3157  df-bdc 14990

This theorem is referenced by: (None)