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- 1 assume (p => q) & (-p => r) & (s => -r) & (s =>
- -q).
- 2 assume s.
- 3 (p => q) & (-p => r) & (s => -r). &E1 1
- 4 s => -q. &E2 1
- 5 (p => q) & (-p => r). &E1 3
- 6 s => -r. &E2 3
- 7 p => q. &E1 5
- 8 -p => r. &E2 5
- 9 assume p.
- 10 -q. =>E 4,2
- 11 q. =>E 7,9
- 12 F. =>E 10,11
- 13 therefore -p. =>I 9,12
- 14 r. =>E 8,13
- 15 -r. =>E 6,2
- 16 F. =>E 15,14
- 17 t. Efq 16
- 18 therefore s => t. =>I 2,17
- 19 therefore (p => q) & (-p => r) & (s => -r) &
- (s => -q) => s => t. =>I 1,18
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