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Theorem tpnz 4121
Description: A triplet containing a set is not empty. (Contributed by NM, 10-Apr-1994.)
Hypothesis
Ref Expression
tpnz.1  |-  A  e. 
_V
Assertion
Ref Expression
tpnz  |-  { A ,  B ,  C }  =/=  (/)

Proof of Theorem tpnz
StepHypRef Expression
1 tpnz.1 . . 3  |-  A  e. 
_V
21tpid1 4113 . 2  |-  A  e. 
{ A ,  B ,  C }
32ne0ii 3768 1  |-  { A ,  B ,  C }  =/=  (/)
Colors of variables: wff setvar class
Syntax hints:    e. wcel 1872    =/= wne 2614   _Vcvv 3080   (/)c0 3761   {ctp 4002
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-v 3082  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3999  df-pr 4001  df-tp 4003
This theorem is referenced by: (None)
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