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Theorem suceqd 42646
Description: Deduction associated with suceq 6410. (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 6410 . 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 1541  suc csuc 6346
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2702
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2709  df-cleq 2723  df-clel 2809  df-v 3468  df-un 3940  df-sn 4614  df-suc 6350
This theorem is referenced by:  scottrankd  42690
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