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
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