Definition df-s5 14793

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 14786	. 2 class ⟨“𝐴𝐵𝐶𝐷𝐸”⟩
7	1, 2, 3, 4	cs4 14785	. . 3 class ⟨“𝐴𝐵𝐶𝐷”⟩
8	5	cs1 14536	. . 3 class ⟨“𝐸”⟩
9		cconcat 14511	. . 3 class ++
10	7, 8, 9	co 7369	. 2 class (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)
11	6, 10	wceq 1540	1 wff ⟨“𝐴𝐵𝐶𝐷𝐸”⟩ = (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)

This definition is referenced by:  s5eqd  14808  s5cld  14816  s5cli  14825  s5len  14842  s1s4  14867  s1s5  14868  s4s2  14872  s5s2  14877  konigsberglem1  30154  konigsberglem2  30155  konigsberglem3  30156  gpgprismgr4cycllem6  48063  gpgprismgr4cycllem7  48064  gpgprismgr4cycllem10  48067