Definition df-s1 14532

Description: Define the canonical injection from symbols to words. Although not required, 𝐴 should usually be a set. Otherwise, the singleton word ⟨“𝐴”⟩ would be the singleton word consisting of the empty set, see s1prc 14540, and not, as maybe expected, the empty word, see also s1nz 14543. (Contributed by Stefan O'Rear, 15-Aug-2015.) (Revised by Mario Carneiro, 26-Feb-2016.)

Assertion

Ref	Expression
df-s1	⊢ ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}

Detailed syntax breakdown of Definition df-s1

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	cs1 14531	. 2 class ⟨“𝐴”⟩
3		cc0 11038	. . . 4 class 0
4		cid 5526	. . . . 5 class I
5	1, 4	cfv 6500	. . . 4 class ( I ‘𝐴)
6	3, 5	cop 4588	. . 3 class ⟨0, ( I ‘𝐴)⟩
7	6	csn 4582	. 2 class {⟨0, ( I ‘𝐴)⟩}
8	2, 7	wceq 1542	1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}

This definition is referenced by:  ids1  14533  s1val  14534  s1eq  14536  s1len  14542  s1nz  14543  funcnvs1  14847