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Mirrors > Home > MPE Home > Th. List > Mathboxes > dp2eq12i | 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 |
dp2eq12i.2 | ⊢ 𝐶 = 𝐷 |
Ref | Expression |
---|---|
dp2eq12i | ⊢ _𝐴𝐶 = _𝐵𝐷 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dp2eq1i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 1 | dp2eq1i 29582 | . 2 ⊢ _𝐴𝐶 = _𝐵𝐶 |
3 | dp2eq12i.2 | . . 3 ⊢ 𝐶 = 𝐷 | |
4 | 3 | dp2eq2i 29583 | . 2 ⊢ _𝐵𝐶 = _𝐵𝐷 |
5 | 2, 4 | eqtri 2644 | 1 ⊢ _𝐴𝐶 = _𝐵𝐷 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 _cdp2 29577 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-dp2 29578 |
This theorem is referenced by: (None) |
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