Theorem bj-intnexr 16625

Description: intnexr 4246 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 16612	. 2 |- -. _V e. _V
2		eleq1 2294	. 2 |- ( |^| A = _V -> ( |^| A e. _V <-> _V e. _V ) )
3	1, 2	mtbiri 682	1 |- ( |^| A = _V -> -. |^| A e. _V )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1398   e. wcel 2202   _Vcvv 2803   |^|cint 3933

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 619  ax-in2 620  ax-5 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-13 2204  ax-14 2205  ax-ext 2213  ax-bdn 16533  ax-bdel 16537  ax-bdsep 16600

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2805

This theorem is referenced by: (None)