Theorem tpidm 3620

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 3617	. 2 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴, 𝐴}
2		dfsn2 3536	. 2 ⊢ {𝐴} = {𝐴, 𝐴}
3	1, 2	eqtr4i 2161	1 ⊢ {𝐴, 𝐴, 𝐴} = {𝐴}

Syntax hints:   = wceq 1331  {csn 3522  {cpr 3523  {ctp 3524

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 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 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-pr 3529  df-tp 3530

This theorem is referenced by: (None)