![]() |
Mathbox for Rohan Ridenour |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > suceqd | Structured version Visualization version GIF version |
Description: Deduction associated with suceq 6421. (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 6421 | . 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 1533 suc csuc 6357 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-v 3468 df-un 3946 df-sn 4622 df-suc 6361 |
This theorem is referenced by: scottrankd 43557 |
Copyright terms: Public domain | W3C validator |