Theorem tpidm23 3733

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

Assertion

Ref	Expression
tpidm23	⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Proof of Theorem tpidm23

Step	Hyp	Ref	Expression
1		tprot 3725	. 2 ⊢ {𝐴, 𝐵, 𝐵} = {𝐵, 𝐵, 𝐴}
2		tpidm12 3731	. 2 ⊢ {𝐵, 𝐵, 𝐴} = {𝐵, 𝐴}
3		prcom 3708	. 2 ⊢ {𝐵, 𝐴} = {𝐴, 𝐵}
4	1, 2, 3	3eqtri 2229	1 ⊢ {𝐴, 𝐵, 𝐵} = {𝐴, 𝐵}

Syntax hints:   = wceq 1372  {cpr 3633  {ctp 3634

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-3or 981  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-un 3169  df-sn 3638  df-pr 3639  df-tp 3640

This theorem is referenced by:  tppreq3  3735