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| Mirrors > Home > MPE Home > Th. List > pm2.18 | Structured version Visualization version Unicode version | ||
| Description: Proof by contradiction. Theorem *2.18 of [WhiteheadRussell] p. 103. Also called the Law of Clavius. See also pm2.01 180. (Contributed by NM, 29-Dec-1992.) |
| Ref | Expression |
|---|---|
| pm2.18 |
   
  |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.21 120 |
. . . 4
| |
| 2 | 1 | a2i 14 |
. . 3
|
| 3 | 2 | con4d 114 |
. 2
|
| 4 | 3 | pm2.43i 52 |
1
|
| Colors of variables: wff setvar class |
| Syntax hints: wn 3
wi 4 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
| This theorem is referenced by: pm2.18i 123 pm2.18d 124 pm4.81 381 sumdmdlem2 29278 pm4.81ALT 32546 axc11n11r 32673 |
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