![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > df-s6 | Structured version Visualization version GIF version |
Description: Define the length 6 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
df-s6 | ⊢ ⟨“𝐴𝐵𝐶𝐷𝐸𝐹”⟩ = (⟨“𝐴𝐵𝐶𝐷𝐸”⟩ ++ ⟨“𝐹”⟩) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | cC | . . 3 class 𝐶 | |
4 | cD | . . 3 class 𝐷 | |
5 | cE | . . 3 class 𝐸 | |
6 | cF | . . 3 class 𝐹 | |
7 | 1, 2, 3, 4, 5, 6 | cs6 14798 | . 2 class ⟨“𝐴𝐵𝐶𝐷𝐸𝐹”⟩ |
8 | 1, 2, 3, 4, 5 | cs5 14797 | . . 3 class ⟨“𝐴𝐵𝐶𝐷𝐸”⟩ |
9 | 6 | cs1 14547 | . . 3 class ⟨“𝐹”⟩ |
10 | cconcat 14522 | . . 3 class ++ | |
11 | 8, 9, 10 | co 7402 | . 2 class (⟨“𝐴𝐵𝐶𝐷𝐸”⟩ ++ ⟨“𝐹”⟩) |
12 | 7, 11 | wceq 1533 | 1 wff ⟨“𝐴𝐵𝐶𝐷𝐸𝐹”⟩ = (⟨“𝐴𝐵𝐶𝐷𝐸”⟩ ++ ⟨“𝐹”⟩) |
Colors of variables: wff setvar class |
This definition is referenced by: s6eqd 14820 s6cld 14828 s6cli 14837 s6len 14854 s1s5 14879 s1s6 14880 s4s2 14883 konigsberglem1 29999 konigsberglem2 30000 konigsberglem3 30001 |
Copyright terms: Public domain | W3C validator |