Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  n0ii Unicode version

Theorem n0ii 3371
 Description: If a class has elements, then it is not empty. Inference associated with n0i 3368. (Contributed by BJ, 15-Jul-2021.)
Hypothesis
Ref Expression
n0ii.1
Assertion
Ref Expression
n0ii

Proof of Theorem n0ii
StepHypRef Expression
1 n0ii.1 . 2
2 n0i 3368 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1331   wcel 1480  c0 3363 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-nul 3364 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator