| 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 14874 | . 2 class 〈“𝐴𝐵”〉 |
| 4 | 1 | cs1 14629 | . . 3 class 〈“𝐴”〉 |
| 5 | 2 | cs1 14629 | . . 3 class 〈“𝐵”〉 |
| 6 | cconcat 14603 | . . 3 class ++ | |
| 7 | 4, 5, 6 | co 7408 | . 2 class (〈“𝐴”〉 ++ 〈“𝐵”〉) |
| 8 | 3, 7 | wceq 1567 | 1 wff 〈“𝐴𝐵”〉 = (〈“𝐴”〉 ++ 〈“𝐵”〉) |
| Colors of variables: wff setvar class |
| This definition is referenced by: cats2cat 14895 s2eqd 14896 s2cld 14904 s2cli 14913 s2fv0 14920 s2fv1 14921 s2len 14922 s2prop 14940 s2co 14953 s1s2 14956 s2s2 14962 s4s2 14963 s2s5 14967 s5s2 14968 s2eq2s1eq 14969 swrds2 14973 repsw2 14983 ccatw2s1ccatws2 14987 s2rn 14996 ofs2 15004 gsumws2 18897 efginvrel2 19793 efgredlemc 19811 frgpnabllem1 19939 2pthon3v 30229 konigsberglem1 30540 konigsberglem2 30541 konigsberglem3 30542 cshw1s2 33217 ofcs2 34876 nthrucw 47487 |
| Copyright terms: Public domain | W3C validator |