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Definition df-s1 13533
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 13619, and not, as maybe expected, the empty word, see also s1nz 13622. (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
StepHypRef Expression
1 cA . . 3 class 𝐴
21cs1 13525 . 2 class ⟨“𝐴”⟩
3 cc0 10231 . . . 4 class 0
4 cid 5231 . . . . 5 class I
51, 4cfv 6111 . . . 4 class ( I ‘𝐴)
63, 5cop 4387 . . 3 class ⟨0, ( I ‘𝐴)⟩
76csn 4381 . 2 class {⟨0, ( I ‘𝐴)⟩}
82, 7wceq 1637 1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}
Colors of variables: wff setvar class
This definition is referenced by:  ids1  13612  s1val  13613  s1eq  13615  s1len  13621  s1nz  13622  funcnvs1  13901
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