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Theorem suceqd 43513
Description: Deduction associated with suceq 6421. (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 6421 . 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 1533  suc csuc 6357
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-sn 4622  df-suc 6361
This theorem is referenced by:  scottrankd  43557
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