1.1 KiB
1.1 KiB
| Line | |||
|---|---|---|---|
| 1 | A \implies \lnot B |
Premise | |
| 2 | (B \lor C) \lor D |
Premise | |
| 3 | \lnot C \lor D \implies A |
Premise | |
| 4 | \lnot C |
Premise | |
| 5 | \lnot C \lor D |
From 4 | \lor Intro |
| 6 | A |
From 3 & 5 | \implies Elim Modus Ponens |
| 7 | \lnot B |
From 1 & 6 | \implies Elim Modus Ponens |
| 8 | \lnot B \land \lnot C |
From 2 & 7 | \land Intro |
| 9 | \lnot (B \lor C) |
From 8 | De Morgans Law |
| 10 | D |
From 9 | \lor Elim Disjunctive Syllogism |
| B or C is not true, therefore D must be true from step 2. |