ƒy / (∃x)ƒx EG where the VARIABLE y is free in ƒy in ALL of those places that x is bound in ƒx by the quantifier (∃x) but y may be free in other places in ƒy as well.
ƒa / (∃x)ƒx EG where the CONSTANT a is free in ƒa in ALL of those places that x is bound in ƒx by the quantifier (∃x) but a may be free in other places in ƒa as well.
CORRECT
| 1. | (x)Axy | |
| 2. | (∃y)(x)Axy | 1,EG |
INcorrect
| 1. | (x)Axy | ||
| 2. | (∃x)Axx | 1,EG | X since the (∃x) controls 2 places in line #2 but y is free only once in #1. Besides, one quatifier cannot simply be replaced by the other. |
CORRECT
| 1. | Aa • Ba | |
| 2. | (∃z)[Az • Bz] | 1,EG |
INcorrect
| 1. | Aa • Bb | ||
| 2. | (∃y)[Ay • By] | 1,EG | X since cannot control 2 different individuals with 1 quantifier. |
CORRECT
|
1. 2. 3. |
(∃y)Axyx Axax (∃y)Ayax |
1,EI 2,EG |
| 4. | Ax | ||
| |5. |6. |
Bx (∃x)Ax |
ACP 4,EG |