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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 14748 | . 2 class 〈“𝐴𝐵”〉 |
| 4 | 1 | cs1 14503 | . . 3 class 〈“𝐴”〉 |
| 5 | 2 | cs1 14503 | . . 3 class 〈“𝐵”〉 |
| 6 | cconcat 14477 | . . 3 class ++ | |
| 7 | 4, 5, 6 | co 7346 | . 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 14769 s2eqd 14770 s2cld 14778 s2cli 14787 s2fv0 14794 s2fv1 14795 s2len 14796 s2prop 14814 s2co 14827 s1s2 14830 s2s2 14836 s4s2 14837 s2s5 14841 s5s2 14842 s2eq2s1eq 14843 swrds2 14847 repsw2 14857 ccatw2s1ccatws2 14861 s2rn 14870 ofs2 14878 gsumws2 18750 efginvrel2 19640 efgredlemc 19658 frgpnabllem1 19786 2pthon3v 29922 konigsberglem1 30230 konigsberglem2 30231 konigsberglem3 30232 cshw1s2 32939 ofcs2 34556 |
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