Description: The iota class is a subset of the union of all elements satisfying ph . (Contributed by Mario Carneiro, 24-Dec-2016) Remove dependency on ax-10 , ax-11 , ax-12 . (Revised by SN, 6-Nov-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | iotassuni | |- ( iota x ph ) C_ U. { x | ph } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotauni2 | |- ( E. y { x | ph } = { y } -> ( iota x ph ) = U. { x | ph } ) |
|
2 | eqimss | |- ( ( iota x ph ) = U. { x | ph } -> ( iota x ph ) C_ U. { x | ph } ) |
|
3 | 1 2 | syl | |- ( E. y { x | ph } = { y } -> ( iota x ph ) C_ U. { x | ph } ) |
4 | iotanul2 | |- ( -. E. y { x | ph } = { y } -> ( iota x ph ) = (/) ) |
|
5 | 0ss | |- (/) C_ U. { x | ph } |
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6 | 4 5 | eqsstrdi | |- ( -. E. y { x | ph } = { y } -> ( iota x ph ) C_ U. { x | ph } ) |
7 | 3 6 | pm2.61i | |- ( iota x ph ) C_ U. { x | ph } |