Definition df-s5 14786

Description: Define the length 5 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.)

Assertion

Ref	Expression
df-s5	⊢ ⟨“𝐴𝐵𝐶𝐷𝐸”⟩ = (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)

Detailed syntax breakdown of Definition df-s5

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3		cC	. . 3 class 𝐶
4		cD	. . 3 class 𝐷
5		cE	. . 3 class 𝐸
6	1, 2, 3, 4, 5	cs5 14779	. 2 class ⟨“𝐴𝐵𝐶𝐷𝐸”⟩
7	1, 2, 3, 4	cs4 14778	. . 3 class ⟨“𝐴𝐵𝐶𝐷”⟩
8	5	cs1 14531	. . 3 class ⟨“𝐸”⟩
9		cconcat 14505	. . 3 class ++
10	7, 8, 9	co 7368	. 2 class (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)
11	6, 10	wceq 1542	1 wff ⟨“𝐴𝐵𝐶𝐷𝐸”⟩ = (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)

This definition is referenced by:  s5eqd  14801  s5cld  14809  s5cli  14818  s5len  14835  s1s4  14860  s1s5  14861  s4s2  14865  s5s2  14870  konigsberglem1  30339  konigsberglem2  30340  konigsberglem3  30341  nthrucw  47244  gpgprismgr4cycllem6  48460  gpgprismgr4cycllem7  48461  gpgprismgr4cycllem10  48464