Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-s2 | Structured version Visualization version GIF version |
Description: Define the length 2 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.) |
Ref | Expression |
---|---|
df-s2 | ⊢ 〈“𝐴𝐵”〉 = (〈“𝐴”〉 ++ 〈“𝐵”〉) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | cs2 14203 | . 2 class 〈“𝐴𝐵”〉 |
4 | 1 | cs1 13949 | . . 3 class 〈“𝐴”〉 |
5 | 2 | cs1 13949 | . . 3 class 〈“𝐵”〉 |
6 | cconcat 13922 | . . 3 class ++ | |
7 | 4, 5, 6 | co 7156 | . 2 class (〈“𝐴”〉 ++ 〈“𝐵”〉) |
8 | 3, 7 | wceq 1537 | 1 wff 〈“𝐴𝐵”〉 = (〈“𝐴”〉 ++ 〈“𝐵”〉) |
Colors of variables: wff setvar class |
This definition is referenced by: cats2cat 14224 s2eqd 14225 s2cld 14233 s2cli 14242 s2fv0 14249 s2fv1 14250 s2len 14251 s2prop 14269 s2co 14282 s1s2 14285 s2s2 14291 s4s2 14292 s2s5 14296 s5s2 14297 s2eq2s1eq 14298 swrds2 14302 repsw2 14312 ccatw2s1ccatws2 14316 ccatw2s1ccatws2OLD 14317 ofs2 14331 gsumws2 18007 efginvrel2 18853 efgredlemc 18871 frgpnabllem1 18993 2pthon3v 27722 konigsberglem1 28031 konigsberglem2 28032 konigsberglem3 28033 cshw1s2 30634 ofcs2 31815 |
Copyright terms: Public domain | W3C validator |