Definition df-s4 14889

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 14882	. 2 class ⟨“𝐴𝐵𝐶𝐷”⟩
6	1, 2, 3	cs3 14881	. . 3 class ⟨“𝐴𝐵𝐶”⟩
7	4	cs1 14633	. . 3 class ⟨“𝐷”⟩
8		cconcat 14608	. . 3 class ++
9	6, 7, 8	co 7431	. 2 class (⟨“𝐴𝐵𝐶”⟩ ++ ⟨“𝐷”⟩)
10	5, 9	wceq 1540	1 wff ⟨“𝐴𝐵𝐶𝐷”⟩ = (⟨“𝐴𝐵𝐶”⟩ ++ ⟨“𝐷”⟩)

This definition is referenced by:  s4eqd  14904  s4cld  14912  s4cli  14921  s4fv0  14934  s4fv1  14935  s4fv2  14936  s4fv3  14937  s4len  14938  s4prop  14949  s1s3  14963  s1s4  14964  s2s2  14968  s4s4  14971  s7rn  15004  tgcgr4  28539  konigsberglem1  30271  konigsberglem2  30272  konigsberglem3  30273