(x)ƒx / ƒy UI where the VARIABLE y is free in ƒy in EXACTLY those places that x is bound in ƒx by the quantifier (x)
(x)ƒx / ƒa UI where the CONSTANT a is free in ƒa in EXACTLY those places that x is bound in ƒx by the quantifier (x)
CORRECT
| 1. | (x)Axy |
| 2. | Axy 1,UI |
INcorrect
| 1. | (x)(y)Axy | |
| 2. | (y)Ayy | 1,UI X since the place controlled in #1 by (x) is in #2 bound by a new quantifier. |
CORRECT
| 1. | (x)Axy | |
| 2. | Ayy | 1,UI |
INcorrect
| 1. | (x)(Ax ⊃ Bx) | ||
| 2. | Ax ⊃ By | 1,UI | X since 1 variable in #1 is replaced 2 different ways. |
CORRECT
| 1. | (y)[Aax • By] | |
| 2. | Aax • Ba | 1,UI |
| 3. | Aax • Bx | 1,UI |
| 4. | Aax • By | 1,UI |
| 5. | Aax • Bb | 1,UI |