Definition df-s3 11529

Description: Define the length 3 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016.)

Assertion

Ref	Expression
df-s3	⊢ ⟨“𝐴𝐵𝐶”⟩ = (⟨“𝐴𝐵”⟩ ++ ⟨“𝐶”⟩)

Detailed syntax breakdown of Definition df-s3

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3		cC	. . 3 class 𝐶
4	1, 2, 3	cs3 11522	. 2 class ⟨“𝐴𝐵𝐶”⟩
5	1, 2	cs2 11521	. . 3 class ⟨“𝐴𝐵”⟩
6	3	cs1 11383	. . 3 class ⟨“𝐶”⟩
7		cconcat 11358	. . 3 class ++
8	5, 6, 7	co 6085	. 2 class (⟨“𝐴𝐵”⟩ ++ ⟨“𝐶”⟩)
9	4, 8	wceq 1402	1 wff ⟨“𝐴𝐵𝐶”⟩ = (⟨“𝐴𝐵”⟩ ++ ⟨“𝐶”⟩)

This definition is used by:  s3eqd  11543  s3cld  11551  s3fv0g  11563  s3fv1g  11564  s3fv2g  11565  s1s2d  11566  s1s3d  11567  s2s2d  11572  s4s3d  11574  s3s4d  11575  konigsberglem1  16729  konigsberglem2  16730  konigsberglem3  16731