Theorem suceqd 43425

Description: Deduction associated with suceq 6430. (Contributed by Rohan Ridenour, 8-Aug-2023.)

Hypothesis

Ref	Expression
suceqd.1	⊢ (𝜑 → 𝐴 = 𝐵)

Assertion

Ref	Expression
suceqd	⊢ (𝜑 → suc 𝐴 = suc 𝐵)

Proof of Theorem suceqd

Step	Hyp	Ref	Expression
1		suceqd.1	. 2 ⊢ (𝜑 → 𝐴 = 𝐵)
2		suceq 6430	. 2 ⊢ (𝐴 = 𝐵 → suc 𝐴 = suc 𝐵)
3	1, 2	syl 17	1 ⊢ (𝜑 → suc 𝐴 = suc 𝐵)

Syntax hints:   → wi 4   = wceq 1540  suc csuc 6366

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 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2702

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3475  df-un 3953  df-sn 4629  df-suc 6370

This theorem is referenced by:  scottrankd  43469