MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tpidm Structured version   Unicode version

Theorem tpidm 4042
Description: Unordered triple  { A ,  A ,  A } is just an overlong way to write  { A }. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tpidm  |-  { A ,  A ,  A }  =  { A }

Proof of Theorem tpidm
StepHypRef Expression
1 tpidm12 4039 . 2  |-  { A ,  A ,  A }  =  { A ,  A }
2 dfsn2 3949 . 2  |-  { A }  =  { A ,  A }
31, 2eqtr4i 2448 1  |-  { A ,  A ,  A }  =  { A }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437   {csn 3936   {cpr 3938   {ctp 3940
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 2058  ax-ext 2403
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2410  df-cleq 2416  df-clel 2419  df-nfc 2553  df-v 3019  df-un 3379  df-pr 3939  df-tp 3941
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator