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Theorem tpeq3d 4752
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 4749 . 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 1537  {ctp 4635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-sn 4632  df-tp 4636
This theorem is referenced by:  tpeq123d  4753  fntpb  7229  erngset  40783  erngset-rN  40791
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