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Theorem tpeq2d 3613
 Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypothesis
Ref Expression
tpeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
tpeq2d (𝜑 → {𝐶, 𝐴, 𝐷} = {𝐶, 𝐵, 𝐷})

Proof of Theorem tpeq2d
StepHypRef Expression
1 tpeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 tpeq2 3610 . 2 (𝐴 = 𝐵 → {𝐶, 𝐴, 𝐷} = {𝐶, 𝐵, 𝐷})
31, 2syl 14 1 (𝜑 → {𝐶, 𝐴, 𝐷} = {𝐶, 𝐵, 𝐷})
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1331  {ctp 3529 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 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-tp 3535 This theorem is referenced by:  tpeq123d  3615
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