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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 12328 | . 2 ⊢ (𝐴 = 𝐵 → ;𝐴𝐶 = ;𝐵𝐶) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ;𝐴𝐶 = ;𝐵𝐶 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 ;cdc 12323 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2114 ax-9 2122 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2073 df-clab 2717 df-cleq 2731 df-clel 2818 df-rab 3073 df-v 3425 df-dif 3886 df-un 3888 df-in 3890 df-ss 3900 df-nul 4255 df-if 4457 df-sn 4559 df-pr 4561 df-op 4565 df-uni 4837 df-br 5071 df-iota 6359 df-fv 6409 df-ov 7238 df-dec 12324 |
This theorem is referenced by: deceq12i 12332 decmul10add 12392 1mhdrd 30942 hgt750lem2 32376 sqn5ii 40070 fmtno5lem4 44727 fmtno5fac 44753 |
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