Existential Instantiation

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(∃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.