![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > pm2.53 | GIF version |
Description: Theorem *2.53 of [WhiteheadRussell] p. 107. This holds intuitionistically, although its converse does not (see pm2.54dc 829). (Contributed by NM, 3-Jan-2005.) (Revised by NM, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm2.53 | ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.24 587 | . 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜓)) | |
2 | ax-1 5 | . 2 ⊢ (𝜓 → (¬ 𝜑 → 𝜓)) | |
3 | 1, 2 | jaoi 672 | 1 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 665 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 581 ax-io 666 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ori 678 ord 679 orel1 680 pm2.63 750 notnotrdc 790 dfordc 830 pm5.6r 875 xorbin 1321 19.33b2 1566 onsucelsucexmid 4359 oprabidlem 5694 xnn0nnn0pnf 8810 absle 10583 |
Copyright terms: Public domain | W3C validator |