Theorem bdinex2 16495

Description: Bounded version of inex2 4224. (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 3399	. 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 16494	. 2 |- ( A i^i B ) e. _V
5	1, 4	eqeltri 2304	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 2202   _Vcvv 2802   i^i cin 3199  BOUNDED wbdc 16435

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-bdsep 16479

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-in 3206  df-bdc 16436

This theorem is referenced by:  bdssex  16497