Definition df-s1 14744

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 14752, and not, as maybe expected, the empty word, see also s1nz 14755. (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 14743	. 2 class ⟨“𝐴”⟩
3		cc0 11201	. . . 4 class 0
4		cid 5545	. . . . 5 class I
5	1, 4	cfv 6539	. . . 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  14745  s1val  14746  s1eq  14748  s1len  14754  s1nz  14755  funcnvs1  15064