A 2 4 r b h 2 i 2 i 1 i i p b h 2 i i i i deduction c

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A = { 0 , 2 , 4 , . . . } R B = {h 2 i, 2 i + 1 i | 0 i } P B = {h 2 i, i i | 0 i } Deduction
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(c) X : { ( x ) Rxx, ¬ ( x )( y ) Rxy, ( x )( y ) x = y } S : p ∧ ¬ p C : U C = R C = Deduction { 1 } (1) ( x ) Rxx P { 2 } (2) ¬ ( x )( y ) Rxy P { 3 } (3) ( x )( y ) x = y P { 3 , 4 } (4) ( y ) u = y (3) u EII { 1 } (5) Ruu (1) UI { 3 , 4 } (6) u = y (4) UI {} (7) u = y ( Ruu Ruy ) III { 3 , 4 } (8) u = x (4) UI {} (9) u = x ( Ruy Rxy ) III { 1 , 3 , (10) Rxy (5)(6) TF; 6 4 } (7)(8) { 4 } EIE (9) { 1 , 3 } (11) ( y ) Rxy (10) UG { 1 , 3 } (12) ( x )( y ) Rxy (11) UG { 1 , 2 , 3 } (13) p ∧ ¬ p (2)(12) TF
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