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Definition df-s1 14634
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 14642, and not, as maybe expected, the empty word, see also s1nz 14645. (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 14633 . 2 class ⟨“𝐴”⟩
3 cc0 11155 . . . 4 class 0
4 cid 5577 . . . . 5 class I
51, 4cfv 6561 . . . 4 class ( I ‘𝐴)
63, 5cop 4632 . . 3 class ⟨0, ( I ‘𝐴)⟩
76csn 4626 . 2 class {⟨0, ( I ‘𝐴)⟩}
82, 7wceq 1540 1 wff ⟨“𝐴”⟩ = {⟨0, ( I ‘𝐴)⟩}
Colors of variables: wff setvar class
This definition is referenced by:  ids1  14635  s1val  14636  s1eq  14638  s1len  14644  s1nz  14645  funcnvs1  14951
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