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pfe_13ans

# Y lxy p z lzx 3 4 y lwy 3 ui z lzw 1 2 3 5 z lzw 24

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y ) Lxy P ( z ) Lzx ) { 3 } (4) ( y ) Lwy (3) UI ( z ) Lzw { 1 , 2 , 3 } (5) ( z ) Lzw (2)(4) TF { 1 , 2 , 3 } (6) Luw (5) UI { 1 , 6 2 , 3 } (7) ( y ) Luy (6) EG; { 2 } EIE { 3 } (8) ( y ) Luy ( z ) Lzu (3) UI { 1 , 3 } (9) ( z ) Lzu (7)(8) TF { 1 , 3 } (10) ( u )( z ) Lzu (9) UG

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(b) X : { ( x )( Fx ( y )( ¬ Fy ( z )( Rxz z = y ))) , ( x )( ¬ Fx ( y )( Fy ( z )( Rzx z = y ))) , ( x )( y )( z )(( Pxy Pxz ) y = z ) , ( x )( y )( Fy Pyx ) } S : p ∧ ¬ p B : U B = { 0 , 1 , 2 ,... } ,F 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
(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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y Lxy P z Lzx 3 4 y Lwy 3 UI z Lzw 1 2 3 5 z Lzw 24 TF 1 2...

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