Theorem tpidm13 3722

Description: Unordered triple { A , B , A } is just an overlong way to write { A , B }. (Contributed by David A. Wheeler, 10-May-2015.)

Assertion

Ref	Expression
tpidm13	|- { A , B , A } = { A , B }

Proof of Theorem tpidm13

Step	Hyp	Ref	Expression
1		tprot 3715	. 2 |- { A , A , B } = { A , B , A }
2		tpidm12 3721	. 2 |- { A , A , B } = { A , B }
3	1, 2	eqtr3i 2219	1 |- { A , B , A } = { A , B }

Syntax hints:   = wceq 1364   {cpr 3623   {ctp 3624

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3or 981  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-tp 3630

This theorem is referenced by: (None)