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| 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 14764 | . 2 class 〈“𝐴𝐵”〉 |
| 4 | 1 | cs1 14519 | . . 3 class 〈“𝐴”〉 |
| 5 | 2 | cs1 14519 | . . 3 class 〈“𝐵”〉 |
| 6 | cconcat 14493 | . . 3 class ++ | |
| 7 | 4, 5, 6 | co 7358 | . 2 class (〈“𝐴”〉 ++ 〈“𝐵”〉) |
| 8 | 3, 7 | wceq 1541 | 1 wff 〈“𝐴𝐵”〉 = (〈“𝐴”〉 ++ 〈“𝐵”〉) |
| Colors of variables: wff setvar class |
| This definition is referenced by: cats2cat 14785 s2eqd 14786 s2cld 14794 s2cli 14803 s2fv0 14810 s2fv1 14811 s2len 14812 s2prop 14830 s2co 14843 s1s2 14846 s2s2 14852 s4s2 14853 s2s5 14857 s5s2 14858 s2eq2s1eq 14859 swrds2 14863 repsw2 14873 ccatw2s1ccatws2 14877 s2rn 14886 ofs2 14894 gsumws2 18767 efginvrel2 19656 efgredlemc 19674 frgpnabllem1 19802 2pthon3v 30016 konigsberglem1 30327 konigsberglem2 30328 konigsberglem3 30329 cshw1s2 33042 ofcs2 34702 nthrucw 47130 |
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