Description: A commonly used pattern in the spirit of r19.29 . (Contributed by Thierry Arnoux, 22-Nov-2017) Reduce axiom usage. (Revised by Wolf Lammen, 17-Jun-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | rexlimdva2.1 | |- ( ( ( ph /\ x e. A ) /\ ps ) -> ch ) |
|
r19.29a.1 | |- ( ph -> E. x e. A ps ) |
||
Assertion | r19.29a | |- ( ph -> ch ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimdva2.1 | |- ( ( ( ph /\ x e. A ) /\ ps ) -> ch ) |
|
2 | r19.29a.1 | |- ( ph -> E. x e. A ps ) |
|
3 | 1 | rexlimdva2 | |- ( ph -> ( E. x e. A ps -> ch ) ) |
4 | 2 3 | mpd | |- ( ph -> ch ) |