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Theorem tpeq3d 4226
 Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypothesis
Ref Expression
tpeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
tpeq3d (𝜑 → {𝐶, 𝐷, 𝐴} = {𝐶, 𝐷, 𝐵})

Proof of Theorem tpeq3d
StepHypRef Expression
1 tpeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 tpeq3 4223 . 2 (𝐴 = 𝐵 → {𝐶, 𝐷, 𝐴} = {𝐶, 𝐷, 𝐵})
31, 2syl 17 1 (𝜑 → {𝐶, 𝐷, 𝐴} = {𝐶, 𝐷, 𝐵})
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475  {ctp 4129 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-sn 4126  df-tp 4130 This theorem is referenced by:  tpeq123d  4227  fntpb  6378  erngset  35106  erngset-rN  35114
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