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Theorem oteq3d 4354
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 4351 . 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 1475  cotp 4133
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-ot 4134
This theorem is referenced by:  oteq123d  4355  idafval  16530  coafval  16537  arwlid  16545  arwrid  16546  arwass  16547  efgi  17955  efgtf  17958  efgtval  17959  efgval2  17960  mapdh6bN  36044  mapdh6cN  36045  mapdh6dN  36046  mapdh6gN  36049  hdmap1l6b  36119  hdmap1l6c  36120  hdmap1l6d  36121  hdmap1l6g  36124
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