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| Mirrors > Home > MPE Home > Th. List > deceq1i | Structured version Visualization version GIF version | ||
| Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.) |
| Ref | Expression |
|---|---|
| deceq1i.1 | ⊢ 𝐴 = 𝐵 |
| Ref | Expression |
|---|---|
| deceq1i | ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | deceq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | deceq1 12738 | . 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ;cdc 12733 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 df-dec 12734 |
| This theorem is referenced by: deceq12i 12742 decmul10add 12802 1mhdrd 32898 hgt750lem2 34667 sqn5ii 42321 fmtno5lem4 47543 fmtno5fac 47569 |
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