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Theorem oteq2d 4649
Description: Equality deduction for ordered triples. (Contributed by Mario Carneiro, 11-Jan-2017.)
Hypothesis
Ref Expression
oteq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
oteq2d (𝜑 → ⟨𝐶, 𝐴, 𝐷⟩ = ⟨𝐶, 𝐵, 𝐷⟩)

Proof of Theorem oteq2d
StepHypRef Expression
1 oteq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 oteq2 4646 . 2 (𝐴 = 𝐵 → ⟨𝐶, 𝐴, 𝐷⟩ = ⟨𝐶, 𝐵, 𝐷⟩)
31, 2syl 17 1 (𝜑 → ⟨𝐶, 𝐴, 𝐷⟩ = ⟨𝐶, 𝐵, 𝐷⟩)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1601  cotp 4406
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-ot 4407
This theorem is referenced by:  oteq123d  4651  mapdh9a  37943  mapdh9aOLDN  37944  hdmap1eulem  37976  hdmap1eulemOLDN  37977  hdmapffval  37980  hdmapfval  37981  hdmapval2  37986
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