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Mirrors > Home > MPE Home > Th. List > df-s5 | Structured version Visualization version GIF version |
Description: Define the length 5 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
df-s5 | ⊢ 〈“𝐴𝐵𝐶𝐷𝐸”〉 = (〈“𝐴𝐵𝐶𝐷”〉 ++ 〈“𝐸”〉) |
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 | 1, 2, 3, 4, 5 | cs5 14555 | . 2 class 〈“𝐴𝐵𝐶𝐷𝐸”〉 |
7 | 1, 2, 3, 4 | cs4 14554 | . . 3 class 〈“𝐴𝐵𝐶𝐷”〉 |
8 | 5 | cs1 14298 | . . 3 class 〈“𝐸”〉 |
9 | cconcat 14271 | . . 3 class ++ | |
10 | 7, 8, 9 | co 7277 | . 2 class (〈“𝐴𝐵𝐶𝐷”〉 ++ 〈“𝐸”〉) |
11 | 6, 10 | wceq 1539 | 1 wff 〈“𝐴𝐵𝐶𝐷𝐸”〉 = (〈“𝐴𝐵𝐶𝐷”〉 ++ 〈“𝐸”〉) |
Colors of variables: wff setvar class |
This definition is referenced by: s5eqd 14577 s5cld 14585 s5cli 14594 s5len 14611 s1s4 14636 s1s5 14637 s4s2 14641 s5s2 14646 konigsberglem1 28613 konigsberglem2 28614 konigsberglem3 28615 |
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