Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > festino | GIF version |
Description: "Festino", one of the syllogisms of Aristotelian logic. No 𝜑 is 𝜓, and some 𝜒 is 𝜓, therefore some 𝜒 is not 𝜑. (In Aristotelian notation, EIO-2: PeM and SiM therefore SoP.) (Contributed by David A. Wheeler, 25-Nov-2016.) |
Ref | Expression |
---|---|
festino.maj | ⊢ ∀𝑥(𝜑 → ¬ 𝜓) |
festino.min | ⊢ ∃𝑥(𝜒 ∧ 𝜓) |
Ref | Expression |
---|---|
festino | ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | festino.min | . 2 ⊢ ∃𝑥(𝜒 ∧ 𝜓) | |
2 | festino.maj | . . . . 5 ⊢ ∀𝑥(𝜑 → ¬ 𝜓) | |
3 | 2 | spi 1469 | . . . 4 ⊢ (𝜑 → ¬ 𝜓) |
4 | 3 | con2i 589 | . . 3 ⊢ (𝜓 → ¬ 𝜑) |
5 | 4 | anim2i 334 | . 2 ⊢ ((𝜒 ∧ 𝜓) → (𝜒 ∧ ¬ 𝜑)) |
6 | 1, 5 | eximii 1533 | 1 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 102 ∀wal 1282 ∃wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |