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Mirrors > Home > MPE Home > Th. List > Mathboxes > suceqd | Structured version Visualization version GIF version |
Description: Deduction associated with suceq 6224. (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 6224 | . 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 1538 suc csuc 6161 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-v 3443 df-un 3886 df-sn 4526 df-suc 6165 |
This theorem is referenced by: scottrankd 40956 |
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