Theorem altopeq2 36906

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 2763	. 2 ⊢ 𝐶 = 𝐶
2		altopeq12 36904	. 2 ⊢ ((𝐶 = 𝐶 ∧ 𝐴 = 𝐵) → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)
3	1, 2	mpan 703	1 ⊢ (𝐴 = 𝐵 → ⟪𝐶, 𝐴⟫ = ⟪𝐶, 𝐵⟫)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  ⟪caltop 36898

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5252  ax-pr 5395

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-sn 4589  df-pr 4591  df-altop 36900

This theorem is used by:  sbcaltop  36923