Theorem tpidm 3633

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

Step	Hyp	Ref	Expression
1		tpidm12 3630	. 2 |- { A , A , A } = { A , A }
2		dfsn2 3546	. 2 |- { A } = { A , A }
3	1, 2	eqtr4i 2164	1 |- { A , A , A } = { A }

Syntax hints:   = wceq 1332   {csn 3532   {cpr 3533   {ctp 3534

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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-un 3080  df-pr 3539  df-tp 3540

This theorem is referenced by: (None)