Description: Deduction eliminating an elementhood in an antecedent. (Contributed by AV, 5-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | pm2.61danel.1 | |- ( ( ph /\ A e. B ) -> ps ) |
|
pm2.61danel.2 | |- ( ( ph /\ A e/ B ) -> ps ) |
||
Assertion | pm2.61danel | |- ( ph -> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61danel.1 | |- ( ( ph /\ A e. B ) -> ps ) |
|
2 | pm2.61danel.2 | |- ( ( ph /\ A e/ B ) -> ps ) |
|
3 | df-nel | |- ( A e/ B <-> -. A e. B ) |
|
4 | 3 2 | sylan2br | |- ( ( ph /\ -. A e. B ) -> ps ) |
5 | 1 4 | pm2.61dan | |- ( ph -> ps ) |