Theorem suceqd 44223

Description: Deduction associated with suceq 6450. (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 6450	. 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 6386

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627  df-suc 6390

This theorem is referenced by:  scottrankd  44267