Definition df-s1 14546

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 14554, and not, as maybe expected, the empty word, see also s1nz 14557. (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 14545	. 2 class ⟨“𝐴”⟩
3		cc0 11110	. . . 4 class 0
4		cid 5574	. . . . 5 class I
5	1, 4	cfv 6544	. . . 4 class ( I ‘𝐴)
6	3, 5	cop 4635	. . 3 class ⟨0, ( I ‘𝐴)⟩
7	6	csn 4629	. 2 class {⟨0, ( I ‘𝐴)⟩}
8	2, 7	wceq 1542	1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}

This definition is referenced by:  ids1  14547  s1val  14548  s1eq  14550  s1len  14556  s1nz  14557  funcnvs1  14863