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Theorem suceqd 43641
Description: Deduction associated with suceq 6435. (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 6435 . 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 1534  suc csuc 6371
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-un 3952  df-sn 4630  df-suc 6375
This theorem is referenced by:  scottrankd  43685
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