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Theorem suceqd 44200
Description: Deduction associated with suceq 6452. (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 6452 . 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 1537  suc csuc 6388
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-sn 4632  df-suc 6392
This theorem is referenced by:  scottrankd  44244
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