Theorem bdinex2 13475

Description: Bounded version of inex2 4099. (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 3299	. 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 13474	. 2 |- ( A i^i B ) e. _V
5	1, 4	eqeltri 2230	1 |- ( B i^i A ) e. _V

Syntax hints:   e. wcel 2128   _Vcvv 2712   i^i cin 3101  BOUNDED wbdc 13415

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-bdsep 13459

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-bdc 13416

This theorem is referenced by:  bdssex  13477