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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 12443 | . 2 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
3 | deceq12i.2 | . . 3 ⊢ 𝐶 = 𝐷 | |
4 | 3 | deceq2i 12444 | . 2 ⊢ ;𝐵𝐶 = ;𝐵𝐷 |
5 | 2, 4 | eqtri 2768 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐷 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ;cdc 12436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2015 ax-8 2112 ax-9 2120 ax-ext 2711 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1545 df-fal 1555 df-ex 1787 df-sb 2072 df-clab 2718 df-cleq 2732 df-clel 2818 df-rab 3075 df-v 3433 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-nul 4263 df-if 4466 df-sn 4568 df-pr 4570 df-op 4574 df-uni 4846 df-br 5080 df-iota 6390 df-fv 6440 df-ov 7274 df-dec 12437 |
This theorem is referenced by: 11multnc 12504 2exp340mod341 45154 |
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