Theorem bj-intnexr 13791

Description: intnexr 4130 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-intnexr	|- ( |^| A = _V -> -. |^| A e. _V )

Proof of Theorem bj-intnexr

Step	Hyp	Ref	Expression
1		bj-vprc 13778	. 2 |- -. _V e. _V
2		eleq1 2229	. 2 |- ( |^| A = _V -> ( |^| A e. _V <-> _V e. _V ) )
3	1, 2	mtbiri 665	1 |- ( |^| A = _V -> -. |^| A e. _V )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1343   e. wcel 2136   _Vcvv 2726   |^|cint 3824

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-in1 604  ax-in2 605  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-13 2138  ax-14 2139  ax-ext 2147  ax-bdn 13699  ax-bdel 13703  ax-bdsep 13766

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2728

This theorem is referenced by: (None)