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 I P ( a /x)  x P a does not occur in  x P a does not occur in an

 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)  x P a does not occur in  x P a does not occur in an

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  1. 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 • E • xP • P(a/x)

  2. I • P(a/x) • xP • a does not occur in xP • a does not occur in an • undischarged assumption • Fa Assumption • xFx 2 I

  3. 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

  4. 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 inxP • a does not occur in Q.

  5. 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 inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx

  6. 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 inxP • a does not occur in Q. • xyLyx • yLya • Laa • xLxx • xLxx • xFx • Fa • Fa • Fa

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