Theorem bj-intnexr 15845

Description: intnexr 4195 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 15832	. 2 |- -. _V e. _V
2		eleq1 2268	. 2 |- ( |^| A = _V -> ( |^| A e. _V <-> _V e. _V ) )
3	1, 2	mtbiri 677	1 |- ( |^| A = _V -> -. |^| A e. _V )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1373   e. wcel 2176   _Vcvv 2772   |^|cint 3885

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-in1 615  ax-in2 616  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-13 2178  ax-14 2179  ax-ext 2187  ax-bdn 15753  ax-bdel 15757  ax-bdsep 15820

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774

This theorem is referenced by: (None)