Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bnj1521.1 | |- ( ch -> E. x e. B ph ) |
|
bnj1521.2 | |- ( th <-> ( ch /\ x e. B /\ ph ) ) |
||
bnj1521.3 | |- ( ch -> A. x ch ) |
||
Assertion | bnj1521 | |- ( ch -> E. x th ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1521.1 | |- ( ch -> E. x e. B ph ) |
|
2 | bnj1521.2 | |- ( th <-> ( ch /\ x e. B /\ ph ) ) |
|
3 | bnj1521.3 | |- ( ch -> A. x ch ) |
|
4 | 1 | bnj1196 | |- ( ch -> E. x ( x e. B /\ ph ) ) |
5 | 4 2 3 | bnj1345 | |- ( ch -> E. x th ) |