Definition df-s5 15044

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 15037	. 2 class ⟨“𝐴𝐵𝐶𝐷𝐸”⟩
7	1, 2, 3, 4	cs4 15036	. . 3 class ⟨“𝐴𝐵𝐶𝐷”⟩
8	5	cs1 14783	. . 3 class ⟨“𝐸”⟩
9		cconcat 14756	. . 3 class ++
10	7, 8, 9	co 7451	. 2 class (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)
11	6, 10	wceq 1570	1 wff ⟨“𝐴𝐵𝐶𝐷𝐸”⟩ = (⟨“𝐴𝐵𝐶𝐷”⟩ ++ ⟨“𝐸”⟩)

This definition is used by:  s5eqd  15059  s5cld  15067  s5cli  15076  s5len  15094  s1s4  15119  s1s5  15120  s4s2  15124  s5s2  15129  konigsberglem1  30910  konigsberglem2  30911  konigsberglem3  30912  numtowerdt  48189  gpgprismgr4cycllem6  49471  gpgprismgr4cycllem7  49472  gpgprismgr4cycllem10  49475