Definition df-s4 14064

Description: Define the length 4 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.)

Assertion

Ref	Expression
df-s4	⊢ ⟨“𝐴𝐵𝐶𝐷”⟩ = (⟨“𝐴𝐵𝐶”⟩ ++ ⟨“𝐷”⟩)

Detailed syntax breakdown of Definition df-s4

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	1, 2, 3, 4	cs4 14057	. 2 class ⟨“𝐴𝐵𝐶𝐷”⟩
6	1, 2, 3	cs3 14056	. . 3 class ⟨“𝐴𝐵𝐶”⟩
7	4	cs1 13748	. . 3 class ⟨“𝐷”⟩
8		cconcat 13723	. . 3 class ++
9	6, 7, 8	co 6970	. 2 class (⟨“𝐴𝐵𝐶”⟩ ++ ⟨“𝐷”⟩)
10	5, 9	wceq 1507	1 wff ⟨“𝐴𝐵𝐶𝐷”⟩ = (⟨“𝐴𝐵𝐶”⟩ ++ ⟨“𝐷”⟩)

This definition is referenced by:  s4eqd  14079  s4cld  14087  s4cli  14096  s4fv0  14109  s4fv1  14110  s4fv2  14111  s4fv3  14112  s4len  14113  s4prop  14124  s1s3  14138  s1s4  14139  s2s2  14143  s4s4  14146  tgcgr4  26009  konigsberglem1  27774  konigsberglem2  27775  konigsberglem3  27776