Definition df-s1 14521

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 14529, and not, as maybe expected, the empty word, see also s1nz 14532. (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 14520	. 2 class ⟨“𝐴”⟩
3		cc0 11028	. . . 4 class 0
4		cid 5517	. . . . 5 class I
5	1, 4	cfv 6486	. . . 4 class ( I ‘𝐴)
6	3, 5	cop 4585	. . 3 class ⟨0, ( I ‘𝐴)⟩
7	6	csn 4579	. 2 class {⟨0, ( I ‘𝐴)⟩}
8	2, 7	wceq 1540	1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}

This definition is referenced by:  ids1  14522  s1val  14523  s1eq  14525  s1len  14531  s1nz  14532  funcnvs1  14837