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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
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I • P(a/x) • xP • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • 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 • E • xP • P(a/x)
I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • Fa Assumption • xFx 2 I
I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • Fa Assumption • xFx 2 I • xFxx Assumption • Fbb 1 E • xFxb 2 I
Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q.
Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx
Fa • xGx • Ga • Fa &Ga • x(Fx&Gx) • x(Fx&Gx) • E • xP • P(a/x) • Q • Q • a does not occur in • undischarged assumption • a does not occur inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx • xFx • Fa • Fa • Fa