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Definition df-si 4728
 Description: Define the singleton image of a class. (Contributed by SF, 5-Jan-2015.)
Assertion
Ref Expression
df-si SI A = {x, y zw(x = {z} y = {w} zAw)}
Distinct variable group:   x,A,y,z,w

Detailed syntax breakdown of Definition df-si
StepHypRef Expression
1 cA . . 3 class A
21csi 4720 . 2 class SI A
3 vx . . . . . . . 8 setvar x
43cv 1641 . . . . . . 7 class x
5 vz . . . . . . . . 9 setvar z
65cv 1641 . . . . . . . 8 class z
76csn 3737 . . . . . . 7 class {z}
84, 7wceq 1642 . . . . . 6 wff x = {z}
9 vy . . . . . . . 8 setvar y
109cv 1641 . . . . . . 7 class y
11 vw . . . . . . . . 9 setvar w
1211cv 1641 . . . . . . . 8 class w
1312csn 3737 . . . . . . 7 class {w}
1410, 13wceq 1642 . . . . . 6 wff y = {w}
156, 12, 1wbr 4639 . . . . . 6 wff zAw
168, 14, 15w3a 934 . . . . 5 wff (x = {z} y = {w} zAw)
1716, 11wex 1541 . . . 4 wff w(x = {z} y = {w} zAw)
1817, 5wex 1541 . . 3 wff zw(x = {z} y = {w} zAw)
1918, 3, 9copab 4622 . 2 class {x, y zw(x = {z} y = {w} zAw)}
202, 19wceq 1642 1 wff SI A = {x, y zw(x = {z} y = {w} zAw)}
 Colors of variables: wff setvar class This definition is referenced by:  dfsi2  4751  brsi  4761  brsnsi  5773
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