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Theorem oteq3d 4803
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
oteq3d (𝜑 → ⟨𝐶, 𝐷, 𝐴⟩ = ⟨𝐶, 𝐷, 𝐵⟩)

Proof of Theorem oteq3d
StepHypRef Expression
1 oteq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 oteq3 4800 . 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 1538  cotp 4558
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-sn 4551  df-pr 4553  df-op 4557  df-ot 4559
This theorem is referenced by:  oteq123d  4804  idafval  17317  coafval  17324  arwlid  17332  arwrid  17333  arwass  17334  efgi  18845  efgtf  18848  efgtval  18849  efgval2  18850  mapdh6bN  38978  mapdh6cN  38979  mapdh6dN  38980  mapdh6gN  38983  hdmap1l6b  39052  hdmap1l6c  39053  hdmap1l6d  39054  hdmap1l6g  39057
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