Step |
Hyp |
Ref |
Expression |
1 |
|
eu6 |
|- ( E! x ph <-> E. y A. x ( ph <-> x = y ) ) |
2 |
|
vex |
|- y e. _V |
3 |
2
|
intsn |
|- |^| { y } = y |
4 |
|
abbi1 |
|- ( A. x ( ph <-> x = y ) -> { x | ph } = { x | x = y } ) |
5 |
|
df-sn |
|- { y } = { x | x = y } |
6 |
4 5
|
eqtr4di |
|- ( A. x ( ph <-> x = y ) -> { x | ph } = { y } ) |
7 |
6
|
inteqd |
|- ( A. x ( ph <-> x = y ) -> |^| { x | ph } = |^| { y } ) |
8 |
|
iotaval |
|- ( A. x ( ph <-> x = y ) -> ( iota x ph ) = y ) |
9 |
3 7 8
|
3eqtr4a |
|- ( A. x ( ph <-> x = y ) -> |^| { x | ph } = ( iota x ph ) ) |
10 |
9
|
exlimiv |
|- ( E. y A. x ( ph <-> x = y ) -> |^| { x | ph } = ( iota x ph ) ) |
11 |
1 10
|
sylbi |
|- ( E! x ph -> |^| { x | ph } = ( iota x ph ) ) |