Theorem bdssexi 15549

Description: Bounded version of ssexi 4171. (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 15548	. 2 |- ( A C_ B -> A e. _V )
5	1, 4	ax-mp 5	1 |- A e. _V

Syntax hints:   e. wcel 2167   _Vcvv 2763   C_ wss 3157  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-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178  ax-bdsep 15530

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-in 3163  df-ss 3170  df-bdc 15487

This theorem is referenced by: (None)