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Theorem suceqd 44223
Description: Deduction associated with suceq 6450. (Contributed by Rohan Ridenour, 8-Aug-2023.)
Hypothesis
Ref Expression
suceqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
suceqd (𝜑 → suc 𝐴 = suc 𝐵)

Proof of Theorem suceqd
StepHypRef Expression
1 suceqd.1 . 2 (𝜑𝐴 = 𝐵)
2 suceq 6450 . 2 (𝐴 = 𝐵 → suc 𝐴 = suc 𝐵)
31, 2syl 17 1 (𝜑 → suc 𝐴 = suc 𝐵)
Colors of variables: wff setvar class
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
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