(∃x)ƒx // ƒa EI 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. | Aay | 1,EI |
INcorrect
| 1. | (∃x)(y)Axy | |
| 2. | (y)Ayy | 1,EI X since the variable bound before the EI MUST be replaced by a constant. |
CORRECT
| 1. | (∃x)Axya | |
| 2. | Abya | 1,EI |
INcorrect
| 1. | (∃x)(Ax ⊃ Bx) | |
| 2. | Aa ⊃ Bb | 1,EI X since the 1 variable in #1 is replaced 2 different ways. |
CORRECT
| 1. | (∃y)[Aa • By] | |
| 2. | Aa • Bb | 1,EI |
| 3. | Aa • Bc | 1,EI |
INcorrect
| 1. | (∃y)[Aa • By] | |
| 2. | Aa • Ba | 1,EI X since the constant that replaces the variable must make its first appearance in the EI line. |