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Mirrors > Home > NFE Home > Th. List > exmid | GIF version |
Description: Law of excluded middle, also called the principle of tertium non datur. Theorem *2.11 of [WhiteheadRussell] p. 101. It says that something is either true or not true; there are no in-between values of truth. This is an essential distinction of our classical logic and is not a theorem of intuitionistic logic. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
exmid | ⊢ (φ ∨ ¬ φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (¬ φ → ¬ φ) | |
2 | 1 | orri 365 | 1 ⊢ (φ ∨ ¬ φ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 357 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-or 359 |
This theorem is referenced by: exmidd 405 pm5.62 889 pm5.63 890 pm4.83 895 4exmid 905 exmidne 2522 rabxm 3573 elimif 3691 |
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