Theorem tpidm 3813

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 3810	. 2 |- { A , A , A } = { A , A }
2		dfsn2 3723	. 2 |- { A } = { A , A }
3	1, 2	eqtr4i 2262	1 |- { A , A , A } = { A }

This proof depends on syntax axioms:   = wceq 1402   {csn 3709   {cpr 3710   {ctp 3711

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-pr 3716  df-tp 3717

This theorem is used by: (None)