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Theorem ne0ii 3430
Description: If a class has elements, then it is nonempty. Inference associated with ne0i 3427. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypothesis
Ref Expression
n0ii.1  |-  A  e.  B
Assertion
Ref Expression
ne0ii  |-  B  =/=  (/)

Proof of Theorem ne0ii
StepHypRef Expression
1 n0ii.1 . 2  |-  A  e.  B
2 ne0i 3427 . 2  |-  ( A  e.  B  ->  B  =/=  (/) )
31, 2ax-mp 5 1  |-  B  =/=  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 2146    =/= wne 2345   (/)c0 3420
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 614  ax-in2 615  ax-io 709  ax-5 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-ne 2346  df-v 2737  df-dif 3129  df-nul 3421
This theorem is referenced by:  pw1ne0  7217  sucpw1nel3  7222
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