Theorem bdssexi 14882

Description: Bounded version of ssexi 4153. (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 14881	. 2 |- ( A C_ B -> A e. _V )
5	1, 4	ax-mp 5	1 |- A e. _V

Syntax hints:   e. wcel 2158   _Vcvv 2749   C_ wss 3141  BOUNDED wbdc 14819

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-bdsep 14863

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-in 3147  df-ss 3154  df-bdc 14820

This theorem is referenced by: (None)