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Theorem oteq3d 4812
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 4809 . 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 1543  cotp 4563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3071  df-v 3422  df-dif 3883  df-un 3885  df-nul 4252  df-if 4454  df-sn 4556  df-pr 4558  df-op 4562  df-ot 4564
This theorem is referenced by:  oteq123d  4813  idafval  17587  coafval  17594  arwlid  17602  arwrid  17603  arwass  17604  efgi  19133  efgtf  19136  efgtval  19137  efgval2  19138  mapdh6bN  39514  mapdh6cN  39515  mapdh6dN  39516  mapdh6gN  39519  hdmap1l6b  39588  hdmap1l6c  39589  hdmap1l6d  39590  hdmap1l6g  39593
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