Theorem bdinex2 10691

Description: Bounded version of inex2 3913. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
bdinex2.bd	|- BOUNDED B
bdinex2.1	|- A e. _V

Assertion

Ref	Expression
bdinex2	|- ( B i^i A ) e. _V

Proof of Theorem bdinex2

Step	Hyp	Ref	Expression
1		incom 3158	. 2 |- ( B i^i A ) = ( A i^i B )
2		bdinex2.bd	. . 3 |- BOUNDED B
3		bdinex2.1	. . 3 |- A e. _V
4	2, 3	bdinex1 10690	. 2 |- ( A i^i B ) e. _V
5	1, 4	eqeltri 2151	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 1433   _Vcvv 2601   i^i cin 2972  BOUNDED wbdc 10631

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063  ax-bdsep 10675

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-in 2979  df-bdc 10632

This theorem is referenced by:  bdssex  10693