i p ( a /x) x p a does not occur in x p a does not occur in an

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I P(a/x) xP a does not occur in xP a does not occur in an undischarged assumption E xP P(a/x) I P(a/x) xP E xP P(a/x) Q Q a does not occur in undischarged assumption a does not occur in xP a does not occur in Q.

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 I P ( a /x)  x P  E  xP P(a/x) Q Q a does not occur in undischarged assumption a does not occur in  xP a does not occur in Q.  I P ( a /x)  x P a does not occur in  x P a does not occur in an undischarged assumption  E  x P P ( a /x).  I - PowerPoint PPT Presentation

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Page 1: I P ( a /x) x P a does not occur in x P a does not occur in an

I

P(a/x)

xP

a does not occur in xP

a does not occur in an

undischarged assumption

E

xP

P(a/x)

I

P(a/x)

xP

E

xP

P(a/x)

Q

Q

a does not occur in

undischarged assumption

a does not occur in xP

a does not occur in Q.

Page 2: I P ( a /x) x P a does not occur in x P a does not occur in an

I

P(a/x)

xP

a does not occur in xP

a does not occur in an

undischarged assumption

1 Fa Assumption

2 xFx 2 I

Page 3: I P ( a /x) x P a does not occur in x P a does not occur in an

I

P(a/x)

xP

a does not occur in xP

a does not occur in an

undischarged assumption

1 Fa Assumption

2 xFx 2 I

1 xFxx Assumption

2 Fbb 1 E

3 xFxb 2 I

Page 4: I P ( a /x) x P a does not occur in x P a does not occur in an

E

xP

P(a/x)

Q

Q

a does not occur in

undischarged assumption

a does not occur in xP

a does not occur in Q.

1. Fa

2. xGx

3. Ga

4. Fa &Ga

5. x(Fx&Gx)

6. x(Fx&Gx)

Page 5: I P ( a /x) x P a does not occur in x P a does not occur in an

E

xP

P(a/x)

Q

Q

a does not occur in

undischarged assumption

a does not occur in xP

a does not occur in Q.

1. Fa

2. xGx

3. Ga

4. Fa &Ga

5. x(Fx&Gx)

6. x(Fx&Gx)

1. xyLyx

2. yLya

3. Laa

4. xLxx

5. xLxx

Page 6: I P ( a /x) x P a does not occur in x P a does not occur in an

E

xP

P(a/x)

Q

Q

a does not occur in

undischarged assumption

a does not occur in xP

a does not occur in Q.

1. Fa

2. xGx

3. Ga

4. Fa &Ga

5. x(Fx&Gx)

6. x(Fx&Gx)

1. xyLyx

2. yLya

3. Laa

4. xLxx

5. xLxx

1. xFx

2. Fa

3. Fa

4. Fa

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