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Mirrors > Home > MPE Home > Th. List > deceq12i | 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 |
deceq12i.2 | ⊢ 𝐶 = 𝐷 |
Ref | Expression |
---|---|
deceq12i | ⊢ ;𝐴𝐶 = ;𝐵𝐷 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | deceq1i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 1 | deceq1i 12093 | . 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
3 | deceq12i.2 | . . 3 ⊢ 𝐶 = 𝐷 | |
4 | 3 | deceq2i 12094 | . 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷 |
5 | 2, 4 | eqtri 2841 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐷 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ;cdc 12086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-3an 1081 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-rex 3141 df-rab 3144 df-v 3494 df-dif 3936 df-un 3938 df-in 3940 df-ss 3949 df-nul 4289 df-if 4464 df-sn 4558 df-pr 4560 df-op 4564 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-ov 7148 df-dec 12087 |
This theorem is referenced by: 11multnc 12154 2exp340mod341 43775 |
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