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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 6387. (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 6387 | . 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 1542 suc csuc 6323 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3449 df-un 3919 df-sn 4591 df-suc 6327 |
This theorem is referenced by: scottrankd 42620 |
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