Definition df-s3 11545

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 11538	. 2 class ⟨“𝐴𝐵𝐶”⟩
5	1, 2	cs2 11537	. . 3 class ⟨“𝐴𝐵”⟩
6	3	cs1 11399	. . 3 class ⟨“𝐶”⟩
7		cconcat 11374	. . 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  11559  s3cld  11567  s3fv0g  11579  s3fv1g  11580  s3fv2g  11581  s1s2d  11582  s1s3d  11583  s2s2d  11588  s4s3d  11590  s3s4d  11591  konigsberglem1  16895  konigsberglem2  16896  konigsberglem3  16897