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Mirrors > Home > MPE Home > Th. List > deceq2OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of deceq1 11376 as of 6-Sep-2021. (Contributed by Mario Carneiro, 17-Apr-2015.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
deceq2OLD | ⊢ (𝐴 = 𝐵 → ;𝐶𝐴 = ;𝐶𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 6557 | . 2 ⊢ (𝐴 = 𝐵 → ((10 · 𝐶) + 𝐴) = ((10 · 𝐶) + 𝐵)) | |
2 | dfdecOLD 11371 | . 2 ⊢ ;𝐶𝐴 = ((10 · 𝐶) + 𝐴) | |
3 | dfdecOLD 11371 | . 2 ⊢ ;𝐶𝐵 = ((10 · 𝐶) + 𝐵) | |
4 | 1, 2, 3 | 3eqtr4g 2669 | 1 ⊢ (𝐴 = 𝐵 → ;𝐶𝐴 = ;𝐶𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1475 (class class class)co 6549 + caddc 9818 · cmul 9820 10c10 10955 ;cdc 11369 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-ov 6552 df-10OLD 10964 df-dec 11370 |
This theorem is referenced by: (None) |
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