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Mirrors > Home > MPE Home > Th. List > 8p1e9 | Structured version Visualization version GIF version |
Description: 8 + 1 = 9. (Contributed by Mario Carneiro, 18-Apr-2015.) |
Ref | Expression |
---|---|
8p1e9 | ⊢ (8 + 1) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-9 11086 | . 2 ⊢ 9 = (8 + 1) | |
2 | 1 | eqcomi 2631 | 1 ⊢ (8 + 1) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 + caddc 9939 8c8 11076 9c9 11077 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-cleq 2615 df-9 11086 |
This theorem is referenced by: cos2bnd 14918 19prm 15825 139prm 15831 317prm 15833 1259lem2 15839 1259lem4 15841 1259lem5 15842 1259prm 15843 2503lem1 15844 2503lem2 15845 2503lem3 15846 4001lem1 15848 quartlem1 24584 log2ub 24676 hgt750lem2 30730 fmtno5lem3 41467 fmtno5lem4 41468 fmtno4prmfac 41484 fmtno5fac 41494 139prmALT 41511 evengpop3 41686 bgoldbtbndlem1 41693 |
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