Theorem bj-intnexr 10700

Description: intnexr 3926 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-intnexr	⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V)

Proof of Theorem bj-intnexr

Step	Hyp	Ref	Expression
1		bj-vprc 10687	. 2 ⊢ ¬ V ∈ V
2		eleq1 2141	. 2 ⊢ (∩ 𝐴 = V → (∩ 𝐴 ∈ V ↔ V ∈ V))
3	1, 2	mtbiri 632	1 ⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1284   ∈ wcel 1433  Vcvv 2601  ∩ cint 3636

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-13 1444  ax-14 1445  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063  ax-bdn 10608  ax-bdel 10612  ax-bdsep 10675

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603

This theorem is referenced by: (None)