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Mathbox for Rohan Ridenour |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > suceqd | Structured version Visualization version GIF version |
Description: Deduction associated with suceq 6430. (Contributed by Rohan Ridenour, 8-Aug-2023.) |
Ref | Expression |
---|---|
suceqd.1 | ⊢ (𝜑 → 𝐴 = 𝐵) |
Ref | Expression |
---|---|
suceqd | ⊢ (𝜑 → suc 𝐴 = suc 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suceqd.1 | . 2 ⊢ (𝜑 → 𝐴 = 𝐵) | |
2 | suceq 6430 | . 2 ⊢ (𝐴 = 𝐵 → suc 𝐴 = suc 𝐵) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → suc 𝐴 = suc 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1540 suc csuc 6366 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-v 3475 df-un 3953 df-sn 4629 df-suc 6370 |
This theorem is referenced by: scottrankd 43469 |
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