Theorem bj-intnexr 16849

Description: intnexr 4282 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 16836	. 2 ⊢ ¬ V ∈ V
2		eleq1 2301	. 2 ⊢ (∩ 𝐴 = V → (∩ 𝐴 ∈ V ↔ V ∈ V))
3	1, 2	mtbiri 686	1 ⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V)

Syntax hints:  ¬ wn 3   → wi 4   = wceq 1402   ∈ wcel 2209  Vcvv 2821  ∩ cint 3965

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 623  ax-in2 624  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-13 2211  ax-14 2212  ax-ext 2220  ax-bdn 16757  ax-bdel 16761  ax-bdsep 16824

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823

This theorem is referenced by: (None)