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Mirrors > Home > MPE Home > Th. List > deceq2i | 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 |
---|---|
deceq2i | ⊢ ;𝐶𝐴 = ;𝐶𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | deceq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | deceq2 12655 | . 2 ⊢ (𝐴 = 𝐵 → ;𝐶𝐴 = ;𝐶𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ;𝐶𝐴 = ;𝐶𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ;cdc 12649 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2702 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2709 df-cleq 2723 df-clel 2809 df-rab 3426 df-v 3468 df-dif 3938 df-un 3940 df-in 3942 df-ss 3952 df-nul 4310 df-if 4514 df-sn 4614 df-pr 4616 df-op 4620 df-uni 4893 df-br 5133 df-iota 6475 df-fv 6531 df-ov 7387 df-dec 12650 |
This theorem is referenced by: deceq12i 12658 sqn5i 40897 |
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