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Mirrors > Home > MPE Home > Th. List > Mathboxes > dp2eq1i | Structured version Visualization version GIF version |
Description: Equality theorem for the decimal expansion constructor. (Contributed by David A. Wheeler, 15-May-2015.) |
Ref | Expression |
---|---|
dp2eq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
dp2eq1i | ⊢ _𝐴𝐶 = _𝐵𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dp2eq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | dp2eq1 30821 | . 2 ⊢ (𝐴 = 𝐵 → _𝐴𝐶 = _𝐵𝐶) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ _𝐴𝐶 = _𝐵𝐶 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 _cdp2 30819 |
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 2018 ax-8 2114 ax-9 2122 ax-ext 2708 |
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 2715 df-cleq 2728 df-clel 2809 df-rab 3060 df-v 3400 df-dif 3856 df-un 3858 df-in 3860 df-ss 3870 df-nul 4224 df-if 4426 df-sn 4528 df-pr 4530 df-op 4534 df-uni 4806 df-br 5040 df-iota 6316 df-fv 6366 df-ov 7194 df-dp2 30820 |
This theorem is referenced by: dp2eq12i 30825 |
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