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Theorem bj-intexr 7131
Description: vnex 3864 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-intexr ( A V → A ≠ ∅)

Proof of Theorem bj-intexr
StepHypRef Expression
1 bj-vprc 7119 . . 3 ¬ V V
2 inteq 3592 . . . . 5 (A = ∅ → A = ∅)
3 int0 3603 . . . . 5 ∅ = V
42, 3syl6eq 2070 . . . 4 (A = ∅ → A = V)
54eleq1d 2088 . . 3 (A = ∅ → ( A V ↔ V V))
61, 5mtbiri 587 . 2 (A = ∅ → ¬ A V)
76necon2ai 2237 1 ( A V → A ≠ ∅)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228   wcel 1374  wne 2186  Vcvv 2535  c0 3201   cint 3589
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-bdn 7044  ax-bdel 7048  ax-bdsep 7111
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ne 2188  df-ral 2289  df-v 2537  df-dif 2897  df-nul 3202  df-int 3590
This theorem is referenced by: (None)
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