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.

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

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

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)

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

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