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Theorem altopeq2 31241
 Description: Equality for alternate ordered pairs. (Contributed by Scott Fenton, 22-Mar-2012.)
Assertion
Ref Expression
altopeq2 (𝐴 = 𝐵 → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)

Proof of Theorem altopeq2
StepHypRef Expression
1 eqid 2610 . 2 𝐶 = 𝐶
2 altopeq12 31239 . 2 ((𝐶 = 𝐶𝐴 = 𝐵) → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)
31, 2mpan 702 1 (𝐴 = 𝐵 → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475  ⟪caltop 31233 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-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  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-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-sn 4126  df-pr 4128  df-altop 31235 This theorem is referenced by:  sbcaltop  31258
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