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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 14482 | . 2 class 〈“𝐴𝐵”〉 |
4 | 1 | cs1 14228 | . . 3 class 〈“𝐴”〉 |
5 | 2 | cs1 14228 | . . 3 class 〈“𝐵”〉 |
6 | cconcat 14201 | . . 3 class ++ | |
7 | 4, 5, 6 | co 7255 | . 2 class (〈“𝐴”〉 ++ 〈“𝐵”〉) |
8 | 3, 7 | wceq 1539 | 1 wff 〈“𝐴𝐵”〉 = (〈“𝐴”〉 ++ 〈“𝐵”〉) |
Colors of variables: wff setvar class |
This definition is referenced by: cats2cat 14503 s2eqd 14504 s2cld 14512 s2cli 14521 s2fv0 14528 s2fv1 14529 s2len 14530 s2prop 14548 s2co 14561 s1s2 14564 s2s2 14570 s4s2 14571 s2s5 14575 s5s2 14576 s2eq2s1eq 14577 swrds2 14581 repsw2 14591 ccatw2s1ccatws2 14595 ccatw2s1ccatws2OLD 14596 ofs2 14610 gsumws2 18396 efginvrel2 19248 efgredlemc 19266 frgpnabllem1 19389 2pthon3v 28209 konigsberglem1 28517 konigsberglem2 28518 konigsberglem3 28519 cshw1s2 31134 ofcs2 32424 |
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