This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Closed form of 19.41 from the same axioms as 19.41v . The same is
doable with 19.27 , 19.28 , 19.31 , 19.32 , 19.44 , 19.45 .
(Contributed by BJ, 2-Dec-2023)
|
|
Ref |
Expression |
|
Assertion |
bj-19.41t |
|- ( F// x ps -> ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
exancom |
|- ( E. x ( ph /\ ps ) <-> E. x ( ps /\ ph ) ) |
| 2 |
|
bj-19.42t |
|- ( F// x ps -> ( E. x ( ps /\ ph ) <-> ( ps /\ E. x ph ) ) ) |
| 3 |
1 2
|
bitrid |
|- ( F// x ps -> ( E. x ( ph /\ ps ) <-> ( ps /\ E. x ph ) ) ) |
| 4 |
3
|
biancomd |
|- ( F// x ps -> ( E. x ( ph /\ ps ) <-> ( E. x ph /\ ps ) ) ) |