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Theorem oteq3 4889
Description: Equality theorem for ordered triples. (Contributed by NM, 3-Apr-2015.)
Assertion
Ref Expression
oteq3 (𝐴 = 𝐵 → ⟨𝐶, 𝐷, 𝐴⟩ = ⟨𝐶, 𝐷, 𝐵⟩)

Proof of Theorem oteq3
StepHypRef Expression
1 opeq2 4879 . 2 (𝐴 = 𝐵 → ⟨⟨𝐶, 𝐷⟩, 𝐴⟩ = ⟨⟨𝐶, 𝐷⟩, 𝐵⟩)
2 df-ot 4640 . 2 𝐶, 𝐷, 𝐴⟩ = ⟨⟨𝐶, 𝐷⟩, 𝐴
3 df-ot 4640 . 2 𝐶, 𝐷, 𝐵⟩ = ⟨⟨𝐶, 𝐷⟩, 𝐵
41, 2, 33eqtr4g 2800 1 (𝐴 = 𝐵 → ⟨𝐶, 𝐷, 𝐴⟩ = ⟨𝐶, 𝐷, 𝐵⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  cop 4637  cotp 4639
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-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-ot 4640
This theorem is referenced by:  oteq3d  4892  otsndisj  5529  otiunsndisj  5530  xpord3pred  8176  efgi0  19753  efgi1  19754  mapdhcl  41710  mapdh6dN  41722  mapdh8  41771  mapdh9a  41772  mapdh9aOLDN  41773  hdmap1l6d  41796  hdmapval  41811  hdmapval2  41815  hdmapval3N  41821  otiunsndisjX  47229
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