Theorem ne0ii 3336

Description: If a class has elements, then it is nonempty. Inference associated with ne0i 3333. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

Ref	Expression
n0ii.1	|- A e. B

Assertion

Ref	Expression
ne0ii	|- B =/= (/)

Proof of Theorem ne0ii

Step	Hyp	Ref	Expression
1		n0ii.1	. 2 |- A e. B
2		ne0i 3333	. 2 |- ( A e. B -> B =/= (/) )
3	1, 2	ax-mp 7	1 |- B =/= (/)

Syntax hints:   e. wcel 1461   =/= wne 2280   (/)c0 3327

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-ne 2281  df-v 2657  df-dif 3037  df-nul 3328

This theorem is referenced by: (None)