Theorem altopeq2 36107

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

Step	Hyp	Ref	Expression
1		eqid 2734	. 2 ⊢ 𝐶 = 𝐶
2		altopeq12 36105	. 2 ⊢ ((𝐶 = 𝐶 ∧ 𝐴 = 𝐵) → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)
3	1, 2	mpan 690	1 ⊢ (𝐴 = 𝐵 → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)

Syntax hints:   → wi 4   = wceq 1541  ⟪caltop 36099

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-sep 5239  ax-nul 5249  ax-pr 5375

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-sn 4579  df-pr 4581  df-altop 36101

This theorem is referenced by:  sbcaltop  36124