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Theorem tpeq2d 4743
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 4740 . 2 (𝐴 = 𝐵 → {𝐶, 𝐴, 𝐷} = {𝐶, 𝐵, 𝐷})
31, 2syl 17 1 (𝜑 → {𝐶, 𝐴, 𝐷} = {𝐶, 𝐵, 𝐷})
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541  {ctp 4626
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-un 3949  df-sn 4623  df-pr 4625  df-tp 4627
This theorem is referenced by:  tpeq123d  4745  fntpb  7195  erngset  39476  erngset-rN  39484
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