Definition df-s1 14736

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 14744, and not, as maybe expected, the empty word, see also s1nz 14747. (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 14735	. 2 class ⟨“𝐴”⟩
3		cc0 11193	. . . 4 class 0
4		cid 5545	. . . . 5 class I
5	1, 4	cfv 6537	. . . 4 class ( I ‘𝐴)
6	3, 5	cop 4590	. . 3 class ⟨0, ( I ‘𝐴)⟩
7	6	csn 4584	. 2 class {⟨0, ( I ‘𝐴)⟩}
8	2, 7	wceq 1570	1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}

This definition is used by:  ids1  14737  s1val  14738  s1eq  14740  s1len  14746  s1nz  14747  funcnvs1  15056